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Volumn 12, Issue , 2007, Pages 420-446

Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct

Author keywords

Continuous state branching process; H transform; Immigration; L vy process; Q process; Quasi stationary distribution; Size biased distribution; Stochastic differential equations; Theorem

Indexed keywords


EID: 34147104061     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v12-402     Document Type: Article
Times cited : (101)

References (43)
  • 1
    • 0742283826 scopus 로고    scopus 로고
    • Change of measures for Markov chains and the L log L theorem for branching processes
    • Athreya, K.B. (2000) Change of measures for Markov chains and the L log L theorem for branching processes. Bernoulli 6 323-338.
    • (2000) Bernoulli , vol.6 , pp. 323-338
    • Athreya, K.B.1
  • 4
    • 0001420276 scopus 로고
    • Continuous branching processes and spectral positivity
    • Bingham, N.H. (1976) Continuous branching processes and spectral positivity. Stoch. Proc. Appl. 4 217-242.
    • (1976) Stoch. Proc. Appl , vol.4 , pp. 217-242
    • Bingham, N.H.1
  • 6
    • 0030295813 scopus 로고    scopus 로고
    • Conditionings and path decompositions for Levy processes
    • Chaumont, L. (1996) Conditionings and path decompositions for Levy processes. Stoch. Proc. Appl. 64 39-54.
    • (1996) Stoch. Proc. Appl. , vol.64 , pp. 39-54
    • Chaumont, L.1
  • 7
    • 33746176613 scopus 로고    scopus 로고
    • Skew convolution semigroups and affine Markov processes
    • Dawson, D.A., Li, Z.-H. (2006) Skew convolution semigroups and affine Markov processes. Ann. Probab. 34 1103-1142.
    • (2006) Ann. Probab , vol.34 , pp. 1103-1142
    • Dawson, D.A.1    Li, Z.-H.2
  • 8
    • 34147098189 scopus 로고    scopus 로고
    • Continuum random trees and branching processes with immigration
    • Duquesne, T. (2007) Continuum random trees and branching processes with immigration. Stoch. Proc. Appl. In press.
    • (2007) Stoch. Proc. Appl
    • Duquesne, T.1
  • 9
    • 33947725198 scopus 로고    scopus 로고
    • Random Trees, Lévy Processes and Spatial Branching Processes
    • Duquesne, T., Le Gall, J.-F. (2002) Random Trees, Lévy Processes and Spatial Branching Processes. Asterisque 281.
    • (2002) Asterisque , pp. 281
    • Duquesne, T.1    Le Gall, J.-F.2
  • 10
    • 0141888171 scopus 로고    scopus 로고
    • A decomposition of the (1+^)-superprocess conditioned on survival
    • Etheridge, A., Williams, D.R.E. (2003) A decomposition of the (1+^)-superprocess conditioned on survival. Proc. Roy. Soc. Edinburgh A 133 829-847.
    • (2003) Proc. Roy. Soc. Edinburgh A , vol.133 , pp. 829-847
    • Etheridge, A.1    Williams, D.R.E.2
  • 11
    • 0009967124 scopus 로고
    • The entrance space of a measure-valued Markov branching process conditioned on nonextinction
    • Evans, S.N. (1992) The entrance space of a measure-valued Markov branching process conditioned on nonextinction. Can. Math. Bull. 35 70-74.
    • (1992) Can. Math. Bull. , vol.35 , pp. 70-74
    • Evans, S.N.1
  • 12
    • 84971790772 scopus 로고
    • Two representations of a conditioned superprocess
    • Evans, S.N. (1993) Two representations of a conditioned superprocess. Proc. Roy. Soc. Edinburgh A 123 959-971.
    • (1993) Proc. Roy. Soc. Edinburgh A , vol.123 , pp. 959-971
    • Evans, S.N.1
  • 13
    • 51249174086 scopus 로고
    • Measure-valued Markov branching processes conditioned on nonextinction
    • Evans, S.N., Perkins, E. (1990) Measure-valued Markov branching processes conditioned on nonextinction. Israel J. Math. 71 329-337.
    • (1990) Israel J. Math , vol.71 , pp. 329-337
    • Evans, S.N.1    Perkins, E.2
  • 14
    • 0002306041 scopus 로고
    • Diffusion processes in genetics
    • U. California Press, Berkeley and Los Angeles
    • Feller, W. (1951) Diffusion processes in genetics. Proc. 2nd Berkeley Symp. Math. Statist. Prob. 227-246. U. California Press, Berkeley and Los Angeles.
    • (1951) Proc. 2Nd Berkeley Symp. Math. Statist. Prob , pp. 227-246
    • Feller, W.1
  • 15
    • 0033235812 scopus 로고    scopus 로고
    • Elementary new proofs of classical limit theorems for Galton-Watson processes
    • Geiger, J. (1999) Elementary new proofs of classical limit theorems for Galton-Watson processes. J. Appl. Prob. 36 301-309.
    • (1999) J. Appl. Prob , vol.36 , pp. 301-309
    • Geiger, J.1
  • 16
    • 0010191693 scopus 로고
    • Asymptotic behaviour of continuous-time, continuous state-space branching processes
    • Grey, D.R. (1974) Asymptotic behaviour of continuous-time, continuous state-space branching processes. J. Appl. Prob. 11 669-677.
    • (1974) J. Appl. Prob , vol.11 , pp. 669-677
    • Grey, D.R.1
  • 17
    • 0001850893 scopus 로고
    • Some mathematical models for branching processes
    • U. California Press, Berkeley and Los Angeles
    • Harris, T.E. (1951) Some mathematical models for branching processes. Proc. 2nd Berkeley Symp. Math. Statist. Prob. 305-328. U. California Press, Berkeley and Los Angeles.
    • (1951) Proc. 2Nd Berkeley Symp. Math. Statist. Prob , pp. 305-328
    • Harris, T.E.1
  • 19
    • 0010174296 scopus 로고
    • Stochastic branching processes with continuous state space
    • Jirina, M. (1958) Stochastic branching processes with continuous state space. Czech. Math. J. 8 292-312.
    • (1958) Czech. Math. J , vol.8 , pp. 292-312
    • Jirina, M.1
  • 20
    • 38249015792 scopus 로고
    • Some time-change representations of stable integrals, via predictable transformations of local martingales
    • Kallenberg, O. (1992) Some time-change representations of stable integrals, via predictable transformations of local martingales. Stoch. Proc. Appl. 40 199-223.
    • (1992) Stoch. Proc. Appl , vol.40 , pp. 199-223
    • Kallenberg, O.1
  • 21
    • 0001782184 scopus 로고
    • Branching processes with immigration and related limit theorems
    • Kawazu, K., Watanabe, S. (1971) Branching processes with immigration and related limit theorems. Teor. Verojanost i Primenen 16 34-51.
    • (1971) Teor. Verojanost I Primenen , vol.16 , pp. 34-51
    • Kawazu, K.1    Watanabe, S.2
  • 25
    • 0036002990 scopus 로고    scopus 로고
    • The genealogy of continuous-state branching processes with immigration
    • Lambert, A. (2002) The genealogy of continuous-state branching processes with immigration. Probab. Theory Relat. Fields 122 (1) 42-70.
    • (2002) Probab. Theory Relat. Fields , vol.122 , Issue.1 , pp. 42-70
    • Lambert, A.1
  • 26
    • 0344944937 scopus 로고    scopus 로고
    • Coalescence times for the branching process
    • Lambert, A. (2003) Coalescence times for the branching process. Adv. Appl. Prob. 35 (4) 1071-1089.
    • (2003) Adv. Appl. Prob. , vol.35 , Issue.4 , pp. 1071-1089
    • Lambert, A.1
  • 27
    • 84968467488 scopus 로고
    • Continuous-state branching processes
    • Lamperti, J. (1967) Continuous-state branching processes. Bull. Amer. Math. Soc. 73 382-386.
    • (1967) Bull. Amer. Math. Soc , vol.73 , pp. 382-386
    • Lamperti, J.1
  • 28
    • 0000005114 scopus 로고
    • Conditioned branching processes and their limiting diffusions
    • Lamperti, J., Ney, P. (1968) Conditioned branching processes and their limiting diffusions. Theor. Probab. Appl. 13 128-139.
    • (1968) Theor. Probab. Appl , vol.13 , pp. 128-139
    • Lamperti, J.1    Ney, P.2
  • 29
    • 0007237457 scopus 로고    scopus 로고
    • Asymptotic behavior of continuous time and state branching processes
    • Li, Z.-H. (2000) Asymptotic behavior of continuous time and state branching processes. J. Aus. Math. Soc. Series A 68 68-84.
    • (2000) J. Aus. Math. Soc. Series A , vol.68 , pp. 68-84
    • Li, Z.-H.1
  • 30
    • 0000028988 scopus 로고
    • Conceptual proofs of L log L criteria for mean behavior of branching processes
    • Lyons, R., Pemantle, R., Peres, Y. (1995) Conceptual proofs of L log L criteria for mean behavior of branching processes. Ann. Probab. 23 1125-1138.
    • (1995) Ann. Probab , vol.23 , pp. 1125-1138
    • Lyons, R.1    Pemantle, R.2    Peres, Y.3
  • 31
    • 21144468256 scopus 로고
    • Conditioned super-Brownian motion
    • Overbeck, L. (1993) Conditioned super-Brownian motion. Probab. Theory Relat. Fields 96 545-570.
    • (1993) Probab. Theory Relat. Fields , vol.96 , pp. 545-570
    • Overbeck, L.1
  • 32
    • 34147119299 scopus 로고
    • Martin boundaries of some branching processes
    • Overbeck, L. (1994) Martin boundaries of some branching processes. Ann. Inst. Henri Poincare Probab. Stat. 30 181-195.
    • (1994) Ann. Inst. Henri Poincare Probab. Stat , vol.30 , pp. 181-195
    • Overbeck, L.1
  • 33
    • 55849093181 scopus 로고    scopus 로고
    • Technical report. To appear in Records and Branching Processes (M. Ahsanullah and G. Yanev Eds) NOVA Science Publishers Inc
    • Pakes, A.G. (1998) Conditional limit theorems for continuous time and state branching processes. Technical report. To appear in Records and Branching Processes (M. Ahsanullah and G. Yanev Eds) NOVA Science Publishers Inc.
    • (1998) Conditional Limit Theorems for Continuous Time and State Branching Processes.
    • Pakes, A.G.1
  • 34
    • 84966232313 scopus 로고
    • Limit theorems for continuous state branching processes with immigration
    • Pinsky, M.A. (1972) Limit theorems for continuous state branching processes with immigration. Bull. Amer. Math. Soc. 78 242-244.
    • (1972) Bull. Amer. Math. Soc , vol.78 , pp. 242-244
    • Pinsky, M.A.1
  • 35
    • 0000674721 scopus 로고
    • A decomposition of Bessel bridges
    • Pitman, J., Yor, M. (1982) A decomposition of Bessel bridges. Z. Wahrsch. verw. Gebiete 59 425-457.
    • (1982) Z. Wahrsch. Verw Gebiete , vol.59 , pp. 425-457
    • Pitman, J.1    Yor, M.2
  • 37
    • 0040100097 scopus 로고
    • Processus de Dawson-Watanabe conditionne par le futur lointain
    • Roelly, S., Rouault, A. (1989) Processus de Dawson-Watanabe conditionne par le futur lointain. C. R. Acad. Sci. Paris Ser. I 30 9 867-872.
    • (1989) C. R. Acad. Sci. Paris Ser. I , vol.30 , Issue.9 , pp. 867-872
    • Roelly, S.1    Rouault, A.2
  • 38
    • 0000564723 scopus 로고
    • On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
    • Seneta, E., Vere-Jones, D. (1966) On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states. J. Appl. Prob. 3 403-434.
    • (1966) J. Appl. Prob , vol.3 , pp. 403-434
    • Seneta, E.1    Vere-Jones, D.2
  • 39
    • 0039983406 scopus 로고
    • On the asymptotic behaviour of subcritical branching processes with continuous state space
    • Seneta, E., Vere-Jones, D. (1968) On the asymptotic behaviour of subcritical branching processes with continuous state space. Z. Wahrsch. verw. Gebiete 10 212-U225.
    • (1968) Z. Wahrsch. Verw Gebiete , vol.10 , pp. U212-U225
    • Seneta, E.1    Vere-Jones, D.2
  • 40
    • 21344436926 scopus 로고    scopus 로고
    • The occupation measure of super-Brownian motion conditioned to nonextinction
    • Serlet, L. (1996) The occupation measure of super-Brownian motion conditioned to nonextinction. J. Theo-ret. Probab. 9 561-578.
    • (1996) J. Theo-Ret. Probab , vol.9 , pp. 561-578
    • Serlet, L.1
  • 41
    • 3943110445 scopus 로고    scopus 로고
    • Multiple scale analysis of spatial branching processes under the Palm distribution
    • Winter, A. (2002) Multiple scale analysis of spatial branching processes under the Palm distribution. Elec. J. Prob. 7 Paper 13.
    • (2002) Elec. J. Prob , vol.7 , Issue.13
    • Winter, A.1
  • 42
    • 0001694745 scopus 로고
    • Certain limit theorems of the theory of branching stochastic processes (In Russian)
    • Yaglom, A.M. (1947) Certain limit theorems of the theory of branching stochastic processes (in Russian). Dokl. Akad. Nauk. SSSR (n.s.) 56 795-798.
    • (1947) Dokl. Akad. Nauk. SSSR (N.S.) , vol.56 , pp. 795-798
    • Yaglom, A.M.1
  • 43
    • 0036018187 scopus 로고    scopus 로고
    • On stochastic differential equations driven by a Cauchy process and other stable Levy motions
    • Zanzotto, P.A. (2002) On stochastic differential equations driven by a Cauchy process and other stable Levy motions. Ann. Probab. 30 802-825
    • (2002) Ann. Probab , vol.30 , pp. 802-825
    • Zanzotto, P.A.1


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