메뉴 건너뛰기




Volumn 4, Issue 1, 2007, Pages 303-364

Branching diffusions, superdiffusions and random media

Author keywords

Branching diffu sions; Catalytic branching; Compact support property; Criticality theory; Law of Large Numbers; Local ex tinction; Measure valued processes; Mild obstacles; Nonlinear h transform; Random environment; Random media; Second order elliptic operators; Spatial branching processes; Spine decomposition; Superprocesses

Indexed keywords


EID: 77952574461     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/07-PS120     Document Type: Article
Times cited : (24)

References (96)
  • 1
    • 0004034112 scopus 로고
    • Measure-Valued Markov Processes
    • Ecole d'Eté Probabilit és de Saint Flour XXI., LNM 1541, . MR1242575
    • Dawson, D. A. (1993) Measure-Valued Markov Processes. Ecole d'Eté Probabilit és de Saint Flour XXI., LNM 1541, 1-260. MR1242575
    • (1993) , pp. 1-260
    • Dawson, D.A.1
  • 2
    • 0003619753 scopus 로고
    • An introduction to branching measure-valued processes
    • CRM Monograph Series, 6. American Mathematical Society, Providence, RI, MR1280712
    • Dynkin, E. B. (1994) An introduction to branching measure-valued processes. CRM Monograph Series, 6. American Mathematical Society, Providence, RI, 134 pp. MR1280712
    • (1994) , pp. 134
    • Dynkin, E.B.1
  • 3
    • 0035470882 scopus 로고    scopus 로고
    • Branching exit Markov systems and superprocesses
    • MR1880244
    • Dynkin, E. B. (2001) Branching exit Markov systems and superprocesses. Ann. Probab. 29(4), 1833-1858. MR1880244
    • (2001) Ann. Probab. , vol.29 , Issue.4 , pp. 1833-1858
    • Dynkin, E.B.1
  • 4
    • 0038934377 scopus 로고    scopus 로고
    • On the construction and support properties of measure-valued diffusions on D ? Rd with spatially dependent branching, Ann
    • MR1698955
    • Engländer, J. and Pinsky, R. (1999) On the construction and support properties of measure-valued diffusions on D ? Rd with spatially dependent branching, Ann. Probab. 27(2), 684-730. MR1698955
    • (1999) Probab. , vol.27 , Issue.2 , pp. 684-730
    • Engländer, J.1    Pinsky, R.2
  • 5
    • 0004266188 scopus 로고    scopus 로고
    • An introduction to superprocesses
    • AMS lecture notes. MR1779100
    • Etheridge, A. (2000) An introduction to superprocesses. AMS lecture notes. MR1779100
    • (2000)
    • Etheridge, A.1
  • 6
    • 51849181398 scopus 로고
    • Construction and regularity of measure-valued Markov branching processes
    • MR0995575
    • Fitzsimmons, P. J. (1988) Construction and regularity of measure-valued Markov branching processes. Israel J. Math. 64(3), 337-361 MR0995575
    • (1988) Israel J. Math. , vol.64 , Issue.3 , pp. 337-361
    • Fitzsimmons, P.J.1
  • 7
    • 0034403735 scopus 로고    scopus 로고
    • The complete characterization of a general class of superprocesses
    • MR1749278
    • Leduc, G. (2000) The complete characterization of a general class of superprocesses. Probab. Theory Related Fields 116(3), 317-358. MR1749278
    • (2000) Probab. Theory Related Fields , vol.116 , Issue.3 , pp. 317-358
    • Leduc, G.1
  • 8
    • 34548528213 scopus 로고    scopus 로고
    • Processus de branchement, arbres et superprocessus
    • (French) [Branching processes, trees and superprocesses] Development of mathematics 1950-2000, Birkhäuser, Basel. MR1796858
    • Le Gall, J.F. (2000) Processus de branchement, arbres et superprocessus. (French) [Branching processes, trees and superprocesses] Development of mathematics 1950-2000, 763-793, Birkhäuser, Basel. MR1796858
    • (2000) , pp. 763-793
    • Le Gall, J.F.1
  • 9
    • 0007202416 scopus 로고    scopus 로고
    • Dawson-Watanabe superprocesses and measure-valued diffusions
    • Lectures on probability theory and statistics (Saint-Flour, 1999), Lecture Notes in Math., 1781, Springer, Berlin. MR1915445
    • Perkins, E. (2002) Dawson-Watanabe superprocesses and measure-valued diffusions. Lectures on probability theory and statistics (Saint-Flour, 1999), 125-324, Lecture Notes in Math., 1781, Springer, Berlin. MR1915445
    • (2002) , pp. 125-324
    • Perkins, E.1
  • 10
    • 0003741894 scopus 로고
    • Positive Harmonic Functions and Diffusion
    • Cambridge University Press. MR1326606
    • Pinsky, R. G. (1995) Positive Harmonic Functions and Diffusion. Cambridge University Press. MR1326606
    • (1995)
    • Pinsky, R.G.1
  • 11
    • 0011676630 scopus 로고
    • Almost-sure path properties of (2, d, ß)-superprocesses
    • MR1288290
    • Dawson, D. A.; Vinogradov, V. (1994) Almost-sure path properties of (2, d, ß)-superprocesses. Stochastic Process. Appl. 51(2), 221-258. MR1288290
    • (1994) Stochastic Process. Appl. , vol.51 , Issue.2 , pp. 221-258
    • Dawson, D.A.1    Vinogradov, V.2
  • 12
    • 0033164058 scopus 로고    scopus 로고
    • Path properties of superprocesses with a general branching mechanism
    • MR1733142
    • Delmas, J.F. (1999) Path properties of superprocesses with a general branching mechanism. Ann. Probab. 27(3), 1099-1134. MR1733142
    • (1999) Ann. Probab. , vol.27 , Issue.3 , pp. 1099-1134
    • Delmas, J.F.1
  • 13
    • 3543009823 scopus 로고    scopus 로고
    • Random trees, Lévy processes and spatial branching processes
    • Astérisque No. 281 MR1954248
    • Duquesne, T. and Le Gall, J.F. (2002) Random trees, Lévy processes and spatial branching processes. Astérisque No. 281 MR1954248
    • (2002)
    • Duquesne, T.1    Le Gall, J.F.2
  • 14
    • 0001417178 scopus 로고
    • Superprocesses and partial differential equations
    • MR1235414
    • Dynkin, E. B. (1993) Superprocesses and partial differential equations. Ann. Probab. 21(3), 1185-1262. MR1235414
    • (1993) Ann. Probab. , vol.21 , Issue.3 , pp. 1185-1262
    • Dynkin, E.B.1
  • 15
    • 7444232848 scopus 로고    scopus 로고
    • Superdiffusions and positive solutions of nonlinear partial differential equations
    • (Appendix A by J.F. Le Gall and Appendix B by I. E. Verbitsky.) University Lecture Series, AmericanMathematical Society, Providence, RI. MR2089791
    • Dynkin, E. B. (2004) Superdiffusions and positive solutions of nonlinear partial differential equations. (Appendix A by J.F. Le Gall and Appendix B by I. E. Verbitsky.) University Lecture Series, 34. AmericanMathematical Society, Providence, RI. MR2089791
    • (2004) , pp. 34
    • Dynkin, E.B.1
  • 16
    • 0010800576 scopus 로고
    • Weighted occupation time for branching particle systems and a representation for the supercritical superprocess
    • MR1275703
    • Evans, S. N.; O'Connell, N. (1994)Weighted occupation time for branching particle systems and a representation for the supercritical superprocess. Canad. Math. Bull. 37(2), 187-196. MR1275703
    • (1994) Canad. Math. Bull. , vol.37 , Issue.2 , pp. 187-196
    • Evans, S.N.1    O'Connell, N.2
  • 17
    • 0034360568 scopus 로고    scopus 로고
    • 2 in Rd for all d ≥ 1-a new probabilistic approach
    • MR1795992
    • 2 in Rd for all d ≥ 1-a new probabilistic approach. Positivity 4, no. 4, 327-337. MR1795992
    • (2000) Positivity , vol.4 , Issue.4 , pp. 327-337
    • Engländer, J.1
  • 18
    • 0038934377 scopus 로고    scopus 로고
    • On the construction and support properties of measure-valued diffusions on D ? Rd with spatially dependent branching, Ann
    • MR1698955
    • Engländer, J. and Pinsky, R. (1999) On the construction and support properties of measure-valued diffusions on D ? Rd with spatially dependent branching, Ann. Probab. 27(2), 684-730. MR1698955
    • (1999) Probab. , vol.27 , Issue.2 , pp. 684-730
    • Engländer, J.1    Pinsky, R.2
  • 19
    • 84890658651 scopus 로고    scopus 로고
    • Random trees and applications
    • (electronic). MR2203728
    • Le Gall, J.F. (2005) Random trees and applications. Probab. Surv. 2, 245- 311 (electronic). MR2203728
    • (2005) Probab. Surv. , vol.2
    • Le Gall, J.F.1
  • 20
    • 1542607824 scopus 로고    scopus 로고
    • Some properties of (a, d, ß)-superprocesses
    • MR1402965
    • Li, C. (1996) Some properties of (a, d, ß)-superprocesses. Acta Math. Sci. (English Ed.) 16(2), 234-240. MR1402965
    • (1996) Acta Math. Sci. (English Ed.) , vol.16 , Issue.2 , pp. 234-240
    • Li, C.1
  • 21
    • 1342288860 scopus 로고    scopus 로고
    • Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation
    • MR2031708
    • Mselati, B. (2004) Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation. Mem. Amer. Math. Soc. 168(798). MR2031708
    • (2004) Mem. Amer. Math. Soc. , vol.168 , Issue.798
    • Mselati, B.1
  • 22
    • 0030486030 scopus 로고    scopus 로고
    • Transience, recurrence and local extinction properties of the support for supercritical finite measure-valued diffusions
    • MR1387634
    • Pinsky, R. G. (1996) Transience, recurrence and local extinction properties of the support for supercritical finite measure-valued diffusions. Ann. Probab. 24(1), 237-267. MR1387634
    • (1996) Ann. Probab. , vol.24 , Issue.1 , pp. 237-267
    • Pinsky, R.G.1
  • 23
    • 0010931534 scopus 로고
    • Asymptotic behavior of superprocesses
    • MR1785007
    • Sheu, Y.C. (1994) Asymptotic behavior of superprocesses. Stochastics Stochastics Rep. 49(3-4), 239-252. MR1785007
    • (1994) Stochastics Stochastics Rep. , vol.49 , Issue.3-4 , pp. 239-252
    • Sheu, Y.C.1
  • 24
    • 0001372549 scopus 로고
    • The behavior of superprocesses near extinction
    • MR1143421
    • Tribe, R. (1992) The behavior of superprocesses near extinction. Ann. Probab. 20(1), 286-311. MR1143421
    • (1992) Ann. Probab. , vol.20 , Issue.1 , pp. 286-311
    • Tribe, R.1
  • 25
    • 0040149001 scopus 로고
    • KPP equation and supercritical branching Brownian motion in the subcritical speed area
    • MR0968823
    • Chauvin, B. and Rouault, A. (1988) KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees. Probab. Theory Related Fields, 80, 299-314. MR0968823
    • (1988) Application to spatial trees. Probab. Theory Related Fields , vol.80 , pp. 299-314
    • Chauvin, B.1    Rouault, A.2
  • 26
    • 17144459686 scopus 로고    scopus 로고
    • Local extinction versus local exponential growth for spatial branching processes, Ann
    • MR2040776
    • Engländer, J. and Kyprianou, A. (2003) Local extinction versus local exponential growth for spatial branching processes, Ann. Probab. 32(1A), 78-99. MR2040776
    • (2003) Probab. , vol.32 A , Issue.1 , pp. 78-99
    • Engländer, J.1    Kyprianou, A.2
  • 27
    • 84971790772 scopus 로고
    • Two representations of a superprocess
    • Proc. Royal. Soc. Edin. . Git, Y.; Harris, MR1249698
    • Evans, S. N. (1993) Two representations of a superprocess. Proc. Royal. Soc. Edin. 123A 959-971. Git, Y.; Harris, MR1249698
    • (1993) , vol.123 A , pp. 959-971
    • Evans, S.N.1
  • 28
    • 51149089970 scopus 로고    scopus 로고
    • Exponential growth rates in a typed branching diffusion
    • MR2308337
    • Git, Y., Harris, J. W. and Harris, S. C. (2007) Exponential growth rates in a typed branching diffusion. Ann. Appl. Probab. 17(2), 609-653. MR2308337
    • (2007) Ann. Appl. Probab. , vol.17 , Issue.2 , pp. 609-653
    • Git, Y.1    Harris, J.W.2    Harris, S.C.3
  • 29
    • 33750605614 scopus 로고    scopus 로고
    • A conceptual approach to a path result for branching Brownian motion
    • MR2307069
    • Hardy, R. and Harris, S. C. (2006) A conceptual approach to a path result for branching Brownian motion. Stoc. Proc. Appl. 116(12), 1992-2013. MR2307069
    • (2006) Stoc. Proc. Appl. , vol.116 , Issue.12 , pp. 1992-2013
    • Hardy, R.1    Harris, S.C.2
  • 30
    • 0000028988 scopus 로고
    • Conceptual proofs of LlogL criteria for mean behavior of branching processes
    • MR1349164
    • Lyons, R., Pemantle R. and Peres, Y. (1995) Conceptual proofs of LlogL criteria for mean behavior of branching processes. Ann. Probab. 23, 1125- 1138. MR1349164
    • (1995) Ann. Probab. , vol.23
    • Lyons, R.1    Pemantle, R.2    Peres, Y.3
  • 31
    • 0001837271 scopus 로고
    • Uniform convergence in the branching random walk, Ann
    • MR1143415
    • Biggins, J. (1992) Uniform convergence in the branching random walk, Ann. Probab., 20, 137-151. MR1143415
    • (1992) Probab. , vol.20 , pp. 137-151
    • Biggins, J.1
  • 32
    • 84890723232 scopus 로고    scopus 로고
    • An almost sure scaling limit theorem for Dawson-Watanabe superprocesses
    • Preprint, electronically available at
    • Chen, ZQ., Ren, Y. and Wang, H. (2007) An almost sure scaling limit theorem for Dawson-Watanabe superprocesses, Preprint, electronically available at http://www.math.washington.edu/~zchen/paper.html
    • (2007)
    • Chen, Z.Q.1    Ren, Y.2    Wang, H.3
  • 33
    • 34547751356 scopus 로고    scopus 로고
    • Limit theorems for branching Markov processes, J
    • MR2352485
    • Chen, ZQ. and Shiozawa Y. (2007) Limit theorems for branching Markov processes, J. Funct. Anal. 250(2), 374-399. MR2352485
    • (2007) Funct. Anal. , vol.250 , Issue.2 , pp. 374-399
    • Chen, Z.Q.1    Shiozawa, Y.2
  • 34
    • 84890764585 scopus 로고    scopus 로고
    • Law of large numbers for superdiffusions: the nonergodic case, to appear in Ann
    • Inst. H. Poincare B.
    • Engländer, J. (2007) Law of large numbers for superdiffusions: the nonergodic case, to appear in Ann. Inst. H. Poincare B.
    • (2007)
    • Engländer, J.1
  • 35
    • 0036018201 scopus 로고    scopus 로고
    • A scaling limit theorem for a class of superdiffusions
    • MR1905855
    • Engländer, J. and Turaev, D. (2002) A scaling limit theorem for a class of superdiffusions. Ann. Probab. 30(2) 683-722. MR1905855
    • (2002) Ann. Probab. , vol.30 , Issue.2 , pp. 683-722
    • Engländer, J.1    Turaev, D.2
  • 36
    • 31444434412 scopus 로고    scopus 로고
    • Law of large numbers for a class of superdiffusions
    • MR2199796
    • Engländer, J. and Winter, A. (2006) Law of large numbers for a class of superdiffusions. Ann. Inst. H. Poincare B, 42(2), 171-185. MR2199796
    • (2006) Ann. Inst. H.Poincare B , vol.42 , Issue.2 , pp. 171-185
    • Engländer, J.1    Winter, A.2
  • 37
    • 84890737147 scopus 로고    scopus 로고
    • Strong Law of Large Numbers for branching diffusions
    • Preprint, electronically available at
    • Engländer, J., Harris, S.C. and Kyprianou A. E. (2007) Strong Law of Large Numbers for branching diffusions, Preprint, electronically available at http://www.pstat.ucsb.edu/faculty/englander/publications.html
    • (2007)
    • Engländer, J.1    Harris, S.C.2    Kyprianou, A.E.3
  • 38
    • 0001686614 scopus 로고
    • A limit theorem of branching processes and continuous state branching processes
    • MR0237008
    • Watanabe, S. (1968) A limit theorem of branching processes and continuous state branching processes. J. Math. Kyoto Univ. 8, 141-167. MR0237008
    • (1968) J. Math. Kyoto Univ. , vol.8 , pp. 141-167
    • Watanabe, S.1
  • 39
    • 84951415984 scopus 로고
    • Problèmes paraboliques semi-linéaires avec données mesures
    • MR0762868
    • Baras, P. and Pierre, M. (1984) Problèmes paraboliques semi-linéaires avec données mesures, Applicable Anal. 18, 111-149. MR0762868
    • (1984) Applicable Anal , vol.18 , pp. 111-149
    • Baras, P.1    Pierre, M.2
  • 40
    • 0000441817 scopus 로고
    • Super-Brownian motion: Path properties and hitting probabilities
    • MR1012498
    • Dawson, D. A., Iscoe, I. and Perkins, E. A. Super-Brownian motion: Path properties and hitting probabilities, Probab. Theory Related Fields 83 (1989), 135-205. MR1012498
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 135-205
    • Dawson, D.A.1    Iscoe, I.2    Perkins, E.A.3
  • 41
    • 0030531421 scopus 로고    scopus 로고
    • Superdiffusions and removable singulari- ties for quasilinear partial differential equations
    • MR1371926
    • Dynkin, E.B. and Kuznetsov, S. Superdiffusions and removable singulari- ties for quasilinear partial differential equations, Comm. Pure Appl. Math. 49 (1996), 125-176. MR1371926
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 125-176
    • Dynkin, E.B.1    Kuznetsov, S.2
  • 42
    • 33748705950 scopus 로고    scopus 로고
    • The compact support property for measure-valued processes
    • MR2259973
    • Engländer, J., Pinsky, Ross G. (2006) The compact support property for measure-valued processes. Ann. Inst. H. Poincaré Probab. Statist. 42(5), 535-552. MR2259973
    • (2006) Ann. Inst. H. Poincaré Probab. Statist. , vol.42 , Issue.5 , pp. 535-552
    • Engländer, J.1    Pinsky, R.G.2
  • 43
    • 0009151742 scopus 로고
    • A note on superprocesses, Probab
    • MR1110534
    • Etheridge, A. and March, P. (1991), A note on superprocesses, Probab. Theory Related Fields, 89(2), 141-147. MR1110534
    • (1991) Theory,Related Fields , vol.89 , Issue.2 , pp. 141-147
    • Etheridge, A.1    March, P.2
  • 44
    • 29144474593 scopus 로고    scopus 로고
    • Positive Solutions of Reaction diffusion equations with super-linear absorption: Universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions, J
    • MR2183378
    • Pinsky, R. (2006) Positive Solutions of Reaction diffusion equations with super-linear absorption: Universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions, J. Differential Equations 220(2), 407-433. MR2183378
    • (2006) Differential Equations , vol.220 , Issue.2 , pp. 407-433
    • Pinsky, R.1
  • 45
    • 84980162898 scopus 로고
    • Asymptotics for the Wiener sausage
    • MR0397901
    • Donsker, M. D., Varadhan, S. R. S. (1975) Asymptotics for the Wiener sausage. Comm. Pure Appl. Math. 28, no. 4, 525-565. MR0397901
    • (1975) Comm. Pure Appl. Math. , vol.28 , Issue.4 , pp. 525-565
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 46
    • 4444291184 scopus 로고
    • Replication of a multicomponent chain by the 'lightning mechanism'
    • Chernov A. A. (1967), Replication of a multicomponent chain by the 'lightning mechanism', Biophysics 12 336 - 341.
    • (1967) Biophysics , vol.12 , pp. 336-341
    • Chernov, A.A.1
  • 47
    • 0001520423 scopus 로고
    • The network model of porous media III
    • Dynamic properties of networks with tube radius distribution. Trans AIME
    • Fatt, I. (1956) The network model of porous media III. Dynamic properties of networks with tube radius distribution. Trans AIME 207, pp. 164-181.
    • (1956) , vol.207 , pp. 164-181
    • Fatt, I.1
  • 48
    • 0002967245 scopus 로고
    • Random walks in a random environment
    • MR0362503
    • Solomon, F. (1975) Random walks in a random environment. Ann. Probability 3, 1-31. MR0362503
    • (1975) Ann. Probability , vol.3 , pp. 1-31
    • Solomon, F.1
  • 49
    • 0003760039 scopus 로고    scopus 로고
    • Brownian motion, obstacles and random media
    • Springer Monographs in Mathematics. Springer-Verlag, Berlin. MR1717054
    • Sznitman, A. (1998) Brownian motion, obstacles and random media. Springer Monographs in Mathematics. Springer-Verlag, Berlin. MR1717054
    • (1998)
    • Sznitman, A.1
  • 50
    • 9144263623 scopus 로고    scopus 로고
    • Topics in random walks in random environment
    • School and Conference on Probability Theory, (electronic), ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste. MR2198849
    • Sznitman, A. (2004) Topics in random walks in random environment. School and Conference on Probability Theory, 203-266 (electronic), ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste. MR2198849
    • (2004) , pp. 203-266
    • Sznitman, A.1
  • 51
    • 0035537281 scopus 로고    scopus 로고
    • On a class of transient random walks in random environment
    • MR1849176
    • Sznitman, A. (2001) On a class of transient random walks in random environment. Ann. Probab. 29(2), 724-765. MR1849176
    • (2001) Ann. Probab. , vol.29 , Issue.2 , pp. 724-765
    • Sznitman, A.1
  • 52
    • 0033212391 scopus 로고    scopus 로고
    • A law of large numbers for random walks in random environment
    • MR1742891
    • Sznitman, A. and Zerner, M. P. W. (1999) A law of large numbers for random walks in random environment. Ann. Probab. 27(4), 1851-1869. MR1742891
    • (1999) Ann. Probab. , vol.27 , Issue.4 , pp. 1851-1869
    • Sznitman, A.1    Zerner, M.P.W.2
  • 53
    • 0033483026 scopus 로고    scopus 로고
    • Slowdown and neutral pockets for a random walk in random environment
    • MR1725386
    • Sznitman, A. (1999) Slowdown and neutral pockets for a random walk in random environment. Probab. Theory Related Fields 115(3), 287-323. MR1725386
    • (1999) Probab. Theory Related Fields , vol.115 , Issue.3 , pp. 287-323
    • Sznitman, A.1
  • 55
    • 4444321966 scopus 로고    scopus 로고
    • Random walks in random environment
    • Lectures on probability theory and statistics, Lecture Notes in Math., 1837, Springer, Berlin. MR2071631
    • Zeitouni, O. (2004) Random walks in random environment. Lectures on probability theory and statistics, 189-312, Lecture Notes in Math., 1837, Springer, Berlin. MR2071631
    • (2004) , pp. 189-312
    • Zeitouni, O.1
  • 56
    • 0035470871 scopus 로고    scopus 로고
    • A zero-one law for planar random walks in random environment
    • MR1880239
    • Zerner, M. P. W. and Merkl, F. (2001) A zero-one law for planar random walks in random environment. Ann. Probab. 29(4), 1716-1732.MR1880239
    • (2001) Ann. Probab. , vol.29 , Issue.4 , pp. 1716-1732
    • Zerner, M.P.W.1    Merkl, F.2
  • 57
    • 0042229249 scopus 로고    scopus 로고
    • Velocity and Lyapounov exponents of some random walks in random environment
    • MR1797391
    • Zerner, Martin P. W. (2000) Velocity and Lyapounov exponents of some random walks in random environment. Ann. Inst. H. Poincaré Probab. Statist. 36(6), 737-748. MR1797391
    • (2000) Ann. Inst. H. Poincaré Probab. Statist. , vol.36 , Issue.6 , pp. 737-748
    • Zerner, M.P.W.1
  • 58
    • 0043209710 scopus 로고    scopus 로고
    • On the volume of the supercritical super-Brownian sausage conditioned on survival, Stochastic Process
    • MR1767846
    • Engländer, J. (2000) On the volume of the supercritical super-Brownian sausage conditioned on survival, Stochastic Process. Appl. 88, 225-243. MR1767846
    • (2000) Appl. , vol.88 , pp. 225-243
    • Engländer, J.1
  • 59
    • 25944434970 scopus 로고    scopus 로고
    • Survival asymptotics for branching Brownian motion in a Poissonian trap field, Markov Process
    • MR2028219
    • Engländer, J., den Hollander, F. (2003) Survival asymptotics for branching Brownian motion in a Poissonian trap field, Markov Process. Related Fields 9, no. 3, 363-389. MR2028219
    • (2003) Related Fields , vol.9 , Issue.3 , pp. 363-389
    • Engländer, J.1    den Hollander, F.2
  • 60
  • 61
    • 0011523712 scopus 로고
    • Minimal displacement of branching random walk
    • MR0510529
    • M. D. Bramson (1978) Minimal displacement of branching random walk. Z. Wahrsch. Verw. Gebiete 45(2), 89-108. MR0510529
    • (1978) Z. Wahrsch. Verw. Gebiete , vol.45 , Issue.2 , pp. 89-108
    • Bramson, M.D.1
  • 62
    • 84980189802 scopus 로고
    • Maximal displacement of branching Brownian motion
    • MR0494541
    • M. D. Bramson (1978) Maximal displacement of branching Brownian motion. Comm. Pure Appl. Math. 31(5), 531-581. MR0494541
    • (1978) Comm. Pure Appl. Math. , vol.31 , Issue.5 , pp. 531-581
    • Bramson, M.D.1
  • 63
    • 2942630398 scopus 로고    scopus 로고
    • Spatial ecology via reaction-diffusion equations
    • Wiley Series in Mathematical and Computational Biology. John Wiley and Sons. MR2191264
    • R. S. Cantrell, C. Cosner (2003) Spatial ecology via reaction-diffusion equations. Wiley Series in Mathematical and Computational Biology. John Wiley and Sons. MR2191264
    • (2003)
    • Cantrell, R.S.1    Cosner, C.2
  • 64
    • 84890782689 scopus 로고    scopus 로고
    • Quenched Law of Large numbers for Branching Brownian motion in a random medium
    • Ann. Inst. H. Poincaré Probab. Statist., to appear
    • Engländer, J. (2007) Quenched Law of Large numbers for Branching Brownian motion in a random medium. Ann. Inst. H. Poincaré Probab. Statist., to appear
    • (2007)
    • Engländer, J.1
  • 65
    • 0003919006 scopus 로고
    • Functional integration and partial differential equations
    • Annals of Mathematics Studies, Princeton University Press. MR0833742
    • M. Freidlin, (1985) Functional integration and partial differential equations. Annals of Mathematics Studies, 109, Princeton University Press. MR0833742
    • (1985) , pp. 109
    • Freidlin, M.1
  • 66
    • 28644438256 scopus 로고    scopus 로고
    • Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation: One sided travelling-waves, Ann
    • MR2196975
    • J. W. Harris, S. C. Harris and A. E. Kyprianou (2006), Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation: One sided travelling-waves, Ann. Inst. H. Poincaré Probab. Statist. 42(1), 125-145. MR2196975
    • (2006) Inst. H. Poincaré Probab. Statist. , vol.42 , Issue.1 , pp. 125-145
    • Harris, J.W.1    Harris, S.C.2    Kyprianou, A.E.3
  • 67
    • 8844287825 scopus 로고    scopus 로고
    • Branching random walk with catalysts
    • (electronic). MR1961167
    • H. Kesten and V. Sidoravicius (2003) Branching random walk with catalysts. Electron. J. Probab. 8(5) (electronic). MR1961167
    • (2003) Electron. J. Probab. , vol.8 , Issue.5
    • Kesten, H.1    Sidoravicius, V.2
  • 68
    • 77951839800 scopus 로고    scopus 로고
    • Asymptotic radial speed of the support of supercritical branching and super-Brownian motion in Rd
    • MR2099406
    • A. E. Kyprianou (2005) Asymptotic radial speed of the support of supercritical branching and super-Brownian motion in Rd. Markov Process. Related Fields. 11(1), 145-156. MR2099406
    • (2005) Markov Process. Related Fields. , vol.11 , Issue.1 , pp. 145-156
    • Kyprianou, A.E.1
  • 69
    • 0032392207 scopus 로고    scopus 로고
    • Wave propagation in a lattice KPP equation in random media, Ann
    • MR1634418
    • T. Y. Lee and F. Torcaso (1998) Wave propagation in a lattice KPP equation in random media, Ann. Probab., 26(3), 1179-1197. MR1634418
    • (1998) Probab. , vol.26 , Issue.3 , pp. 1179-1197
    • Lee, T.Y.1    Torcaso, F.2
  • 70
    • 0034641717 scopus 로고    scopus 로고
    • The importance of being discrete: Life always wins on the surface, Proc
    • N. M. Shnerb, Y. Louzoun, E. Bettelheim and S. Solomon (2000) The importance of being discrete: Life always wins on the surface, Proc. Nat. Acad. Sciences 97, 10322-10324.
    • (2000) Nat. Acad. Sciences , vol.97 , pp. 10322-10324
    • Shnerb, N.M.1    Louzoun, Y.2    Bettelheim, E.3    Solomon, S.4
  • 71
    • 4243971213 scopus 로고    scopus 로고
    • Adaptation of autocatalytic fluctuations to diffusive noise, Phys
    • N. M. Shnerb, E. Bettelheim, Y. Louzoun, O. Agam and S. Solomon (2001) Adaptation of autocatalytic fluctuations to diffusive noise, Phys. Rev. E 63, 21103-21108.
    • (2001) Rev.E , vol.63 , pp. 21103-21108
    • Shnerb, N.M.1    Bettelheim, E.2    Louzoun, Y.3    Agam, O.4    Solomon, S.5
  • 72
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • (electronic) MR1778352
    • J. Xin (2000) Front propagation in heterogeneous media, SIAM Rev. 42(2), 161-230 (electronic) MR1778352
    • (2000) SIAM Rev , vol.42 , Issue.2 , pp. 161-230
    • Xin, J.1
  • 73
    • 84890699760 scopus 로고    scopus 로고
    • Quenched Law of Large numbers for Branching Brownian motion in a random medium
    • to appear
    • Engländer, J. (2007) Quenched Law of Large numbers for Branching Brownian motion in a random medium. Ann. Inst. H. Poincaré Probab. Statist., to appear
    • (2007) Ann. Inst. H. Poincaré Probab. Statist.
    • Engländer, J.1
  • 76
    • 38149143515 scopus 로고
    • A super-Brownian motion with a single point catalyst
    • MR1258279
    • Dawson, D. A.; Fleischmann, K. (1994) A super-Brownian motion with a single point catalyst. Stochastic Process. Appl. 49(1), 3-40. MR1258279
    • (1994) Stochastic Process. Appl. , vol.49 , Issue.1 , pp. 3-40
    • Dawson, D.A.1    Fleischmann, K.2
  • 77
    • 0012498858 scopus 로고    scopus 로고
    • Catalytic and mutually catalytic super-Brownian motions
    • Seminar on Stochastic Analysis, Random Fields and Applications, III (Ascona, 1999), Progr. Probab., 52, Birkhäuser, Basel. MR1958811
    • Dawson, D. A., Fleischmann, K. (2002) Catalytic and mutually catalytic super-Brownian motions. Seminar on Stochastic Analysis, Random Fields and Applications, III (Ascona, 1999), 89-110, Progr. Probab., 52, Birkhäuser, Basel. MR1958811
    • (2002) , pp. 89-110
    • Dawson, D.A.1    Fleischmann, K.2
  • 78
    • 0040941947 scopus 로고    scopus 로고
    • Catalytic and mutually catalytic branching
    • Infinite dimensional stochastic analysis (Amsterdam, 1999), Verh. Afd. Natuurkd. 1. Reeks. K. Ned. Akad. Wet., 52, R. Neth. Acad. Arts Sci., Amsterdam. MR1831416
    • Dawson, D. A. and Fleischmann, K. (2000) Catalytic and mutually catalytic branching. Infinite dimensional stochastic analysis (Amsterdam, 1999), 145-170, Verh. Afd. Natuurkd. 1. Reeks. K. Ned. Akad. Wet., 52, R. Neth. Acad. Arts Sci., Amsterdam. MR1831416
    • (2000) , pp. 145-170
    • Dawson, D.A.1    Fleischmann, K.2
  • 80
    • 0032393494 scopus 로고    scopus 로고
    • Long-time behavior and coexistence in a mutually catalytic branching model
    • MR1634416
    • Dawson, D. A., Perkins, E. A. (1998) Long-time behavior and coexistence in a mutually catalytic branching model. Ann. Probab. 26(3), 1088-1138. MR1634416
    • (1998) Ann. Probab. , vol.26 , Issue.3 , pp. 1088-1138
    • Dawson, D.A.1    Perkins, E.A.2
  • 81
    • 33846820563 scopus 로고    scopus 로고
    • On the uniqueness problem for catalytic branching networks and other singular diffusions
    • (electronic). MR2247832
    • Dawson, D. A. and Perkins, E. A. (2006) On the uniqueness problem for catalytic branching networks and other singular diffusions. Illinois J. Math. 50(1-4), 323-383 (electronic). MR2247832
    • (2006) Illinois J. Math. , vol.50 , Issue.1-4 , pp. 323-383
    • Dawson, D.A.1    Perkins, E.A.2
  • 82
    • 3843145568 scopus 로고    scopus 로고
    • Generalized Mehler semigroups and catalytic branching processes with immigration
    • MR2048508
    • Dawson, D. A., Li, Z., Schmuland, B. and Sun, W. (2004) Generalized Mehler semigroups and catalytic branching processes with immigration. Potential Anal. 21(1), 75-97. MR2048508
    • (2004) Potential Anal. , vol.21 , Issue.1 , pp. 75-97
    • Dawson, D.A.1    Li, Z.2    Schmuland, B.3    Sun, W.4
  • 83
    • 0039951253 scopus 로고
    • Branching with a single point catalyst
    • Stochastic analysis (Ithaca, NY, 1993), Proc. Sympos. Pure Math., 57, Amer. Math. Soc., Providence, RI. MR1335486
    • Dynkin, E. B. (1995) Branching with a single point catalyst. Stochastic analysis (Ithaca, NY, 1993), 423-425, Proc. Sympos. Pure Math., 57, Amer. Math. Soc., Providence, RI. MR1335486
    • (1995) , pp. 423-425
    • Dynkin, E.B.1
  • 84
    • 0031632403 scopus 로고    scopus 로고
    • Persistence of a twodimensional super-Brownian motion in a catalyticmedium
    • MR1602028
    • Etheridge, A. M. and Fleischmann K. (1998) Persistence of a twodimensional super-Brownian motion in a catalyticmedium. Probab. Theory Related Fields 110(1), 1-12. MR1602028
    • (1998) Probab. Theory Related Fields , vol.110 , Issue.1 , pp. 1-12
    • Etheridge, A.M.1    Fleischmann, K.2
  • 85
    • 21844503686 scopus 로고
    • A new approach to the single point catalytic super-Brownian motion
    • MR1351711
    • Fleischmann, K. and Le Gall, J.F. (1995) A new approach to the single point catalytic super-Brownian motion. Probab. Theory Related Fields 102(1), 63-82. MR1351711
    • (1995) Probab. Theory Related Fields , vol.102 , Issue.1 , pp. 63-82
    • Fleischmann, K.1    Le Gall, J.F.2
  • 86
    • 0002050211 scopus 로고    scopus 로고
    • Finite time extinction of catalytic branching processes
    • Stochastic models (Ottawa, ON, 1998), CMS Conf. Proc., 26, Amer. Math. Soc., Providence, RI. MR1765007
    • Fleischmann, K. and Mueller, C. (2000) Finite time extinction of catalytic branching processes. Stochastic models (Ottawa, ON, 1998), 125-139, CMS Conf. Proc., 26, Amer. Math. Soc., Providence, RI. MR1765007
    • (2000) , pp. 125-139
    • Fleischmann, K.1    Mueller, C.2
  • 87
    • 0035537293 scopus 로고    scopus 로고
    • A cyclically catalytic super-Brownian motion
    • MR1849179
    • Fleischmann, K. and Xiong, J. (2001) A cyclically catalytic super-Brownian motion. Ann. Probab. 29(2), 820-861. MR1849179
    • (2001) Ann. Probab. , vol.29 , Issue.2 , pp. 820-861
    • Fleischmann, K.1    Xiong, J.2
  • 88
    • 8844287825 scopus 로고    scopus 로고
    • Branching random walk with catalysts
    • (electronic). MR1961167
    • Kesten, H., Sidoravicius, V. (2003) Branching random walk with catalysts. Electron. J. Probab. 8, no. 5. (electronic). MR1961167
    • (2003) Electron. J. Probab. , vol.8 , Issue.5
    • Kesten, H.1    Sidoravicius, V.2
  • 89
    • 0002133811 scopus 로고    scopus 로고
    • A review on spatial catalytic branching
    • Stochastic models (Ottawa, ON, 1998), CMS Conf. Proc., 26, Amer. Math. Soc., Providence, RI. MR1765014
    • Klenke, A. (2000) A review on spatial catalytic branching. Stochastic models (Ottawa, ON, 1998), 245-263, CMS Conf. Proc., 26, Amer. Math. Soc., Providence, RI. MR1765014
    • (2000) , pp. 245-263
    • Klenke, A.1
  • 90
    • 0037290934 scopus 로고    scopus 로고
    • Catalytic branching and the Brownian snake
    • MR1950764
    • Klenke, A. (2003) Catalytic branching and the Brownian snake. Stochastic Process. Appl. 103(2), 211-235. MR1950764
    • (2003) Stochastic Process. Appl. , vol.103 , Issue.2 , pp. 211-235
    • Klenke, A.1
  • 91
    • 10244260425 scopus 로고    scopus 로고
    • A construction of catalytic super-Brownian motion via collision local time
    • MR2105370
    • Mörters, P., Vogt, P. (2005) A construction of catalytic super-Brownian motion via collision local time. Stochastic Process. Appl. 115(1), 77-90. MR2105370
    • (2005) Stochastic Process. Appl. , vol.115 , Issue.1 , pp. 77-90
    • Mörters, P.1    Vogt, P.2
  • 92
    • 0032187777 scopus 로고    scopus 로고
    • Uniqueness for a mutually catalytic branching model
    • MR1653845
    • Mytnik, L. (1998) Uniqueness for a mutually catalytic branching model. Probab. Theory Related Fields 112(2), 245-253. MR1653845
    • (1998) Probab. Theory Related Fields , vol.112 , Issue.2 , pp. 245-253
    • Mytnik, L.1
  • 93
    • 84862287704 scopus 로고    scopus 로고
    • Two-dimensional limit theorem for a critical catalytic branching random walk
    • Mathematics and computer science. III, , Trends Math., Birkhäuser, Basel. MR2090528
    • Topchii, V. and Vatutin, V. (2004) Two-dimensional limit theorem for a critical catalytic branching random walk. Mathematics and computer science. III, 387-395, Trends Math., Birkhäuser, Basel. MR2090528
    • (2004) , pp. 387-395
    • Topchii, V.1    Vatutin, V.2
  • 94
    • 27144546264 scopus 로고    scopus 로고
    • Individuals at the origin in the critical catalytic branching random walk
    • Discrete random walks (Paris, 2003), (electronic), Discrete Math. Theor. Comput. Sci. Proc., AC, Assoc. Discrete Math. Theor. Comput. Sci., Nancy. MR2042398
    • Topchii, V. and Vatutin, V. (2003) Individuals at the origin in the critical catalytic branching random walk. Discrete random walks (Paris, 2003), 325-332 (electronic), Discrete Math. Theor. Comput. Sci. Proc., AC, Assoc. Discrete Math. Theor. Comput. Sci., Nancy. MR2042398
    • (2003) , pp. 325-332
    • Topchii, V.1    Vatutin, V.2
  • 95
    • 34249111469 scopus 로고    scopus 로고
    • Some limit theorems for a particle system of single point catalytic branching random walks
    • MR2319610
    • Vatutin, V. and Xiong, J. (2007) Some limit theorems for a particle system of single point catalytic branching random walks. Acta Math. Sin. (Engl. Ser.) 23(6), 997-1012. MR2319610
    • (2007) Acta Math. Sin. (Engl. Ser.) , vol.23 , Issue.6 , pp. 997-1012
    • Vatutin, V.1    Xiong, J.2
  • 96
    • 34249063199 scopus 로고    scopus 로고
    • A limit theorem for critical catalytic branching random walks
    • translation in Theory Probab. Appl. 49(3), 498-518. MR2144864, 2004
    • Vatutin, V. A. and Topchiǐ, V. A. (2005) A limit theorem for critical catalytic branching random walks. (Russian) Teor. Veroyatn. Primen. 49 (2004), no. 3, 461-484; translation in Theory Probab. Appl. 49(3), 498-518. MR2144864
    • (2005) (Russian) Teor. Veroyatn. Primen. , vol.49 , Issue.3 , pp. 461-484
    • Vatutin, V.A.1    Topchiǐ, V.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.