메뉴 건너뛰기




Volumn 28, Issue 2, 2000, Pages 603-642

Finite time extinction of superprocesses with catalysts

Author keywords

Catalytic super brownian motion; Collision local time; Comparison; Critical branching; Finite time extinction; Finite time survival; Good and bad paths; Historical superprocess; Measure valued branching; Random medium; Stopped measures

Indexed keywords


EID: 0034345575     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1019160254     Document Type: Article
Times cited : (6)

References (31)
  • 1
    • 0001481374 scopus 로고
    • Collision local times and measure-valued processes
    • BARLOW, M. T., EVANS, S. N. and PERKINS, E. A. (1991). Collision local times and measure-valued processes. Canad. J. Math. 43 897-938.
    • (1991) Canad. J. Math. , vol.43 , pp. 897-938
    • Barlow, M.T.1    Evans, S.N.2    Perkins, E.A.3
  • 3
    • 0001098531 scopus 로고
    • Critical branching in a highly fluctuating random medium
    • DAWSON, D. A. and FLEISCHMANN, K. (1991). Critical branching in a highly fluctuating random medium. Probab. Theory Related Fields 90 241-274.
    • (1991) Probab. Theory Related Fields , vol.90 , pp. 241-274
    • Dawson, D.A.1    Fleischmann, K.2
  • 4
    • 0026819887 scopus 로고
    • Diffusion and reaction caused by point catalysts
    • DAWSON, D. A. and FLEISCHMANN, K. (1992). Diffusion and reaction caused by point catalysts. SIAM J. Appl. Math. 52 163-180.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 163-180
    • Dawson, D.A.1    Fleischmann, K.2
  • 5
    • 0031504086 scopus 로고    scopus 로고
    • A continuous super-Brownian motion in a super-Brownian medium
    • DAWSON, D. A. and FLEISCHMANN, K. (1997). A continuous super-Brownian motion in a super-Brownian medium. J. Theoret. Probab. 10 213-276.
    • (1997) J. Theoret. Probab. , vol.10 , pp. 213-276
    • Dawson, D.A.1    Fleischmann, K.2
  • 7
    • 0032382789 scopus 로고    scopus 로고
    • Continuous dependence of a class of superprocesses on branching parameters and applications
    • DAWSON, D. A., FLEISCHMANN, K. and LEDUC, G. (1998). Continuous dependence of a class of superprocesses on branching parameters and applications. Ann. Probab. 26 262-601.
    • (1998) Ann. Probab. , vol.26 , pp. 262-601
    • Dawson, D.A.1    Fleischmann, K.2    Leduc, G.3
  • 8
    • 0002300687 scopus 로고
    • Absolute continuity for the measure states in a branching model with catalysts
    • DAWSON, D. A., FLEISCHMANN, K. and ROELLY, S. (1991). Absolute continuity for the measure states in a branching model with catalysts. Prog. Probab. 24 117-160.
    • (1991) Prog. Probab. , vol.24 , pp. 117-160
    • Dawson, D.A.1    Fleischmann, K.2    Roelly, S.3
  • 9
    • 21344433853 scopus 로고
    • The support of measure-valued branching processes in a random environment
    • DAWSON, D. A., LI, Y. and MUELLER, C. (1995). The support of measure-valued branching processes in a random environment. Ann. Probab. 23 1692-1718.
    • (1995) Ann. Probab. , vol.23 , pp. 1692-1718
    • Dawson, D.A.1    Li, Y.2    Mueller, C.3
  • 12
    • 84980138040 scopus 로고
    • On laws of the iterated logarithm for local times
    • DONSKER, M. D. and VARADHAN, S. R. (1977). On laws of the iterated logarithm for local times. Comm. Pure Appl. Math. 30 707-753.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 707-753
    • Donsker, M.D.1    Varadhan, S.R.2
  • 14
    • 0000466469 scopus 로고
    • Branching particle systems and superprocesses
    • DYNKIN, E. B. (1991). Branching particle systems and superprocesses. Ann. Probab. 19 1157-1194.
    • (1991) Ann. Probab. , vol.19 , pp. 1157-1194
    • Dynkin, E.B.1
  • 15
    • 0003016819 scopus 로고
    • Path processes and historical superprocesses
    • DYNKIN, E. B. (1991). Path processes and historical superprocesses. Probab. Theory Related Fields 90 1-36.
    • (1991) Probab. Theory Related Fields , vol.90 , pp. 1-36
    • Dynkin, E.B.1
  • 16
    • 0002026562 scopus 로고    scopus 로고
    • Extinction properties of super-Brownian motions with additional spatially dependent mass production
    • ENGLÄNDER, J. and FLEISCHMANN, K. (2000). Extinction properties of super-Brownian motions with additional spatially dependent mass production. Stoch. Process. Appl. 88 37-58.
    • (2000) Stoch. Process. Appl. , vol.88 , pp. 37-58
    • Engländer, J.1    Fleischmann, K.2
  • 17
    • 0033449129 scopus 로고    scopus 로고
    • Smooth density field of catalytic super-Brownian motion
    • FLEISCHMANN, K. and KLENKE, A. (1999). Smooth density field of catalytic super-Brownian motion. Ann. Appl. Probab. 9 298-318.
    • (1999) Ann. Appl. Probab. , vol.9 , pp. 298-318
    • Fleischmann, K.1    Klenke, A.2
  • 18
    • 0034310126 scopus 로고    scopus 로고
    • The biodiversity of catalytic super-Brownian motion
    • To appear
    • FLEISCHMANN, K. and KLENKE, A. (2000). The biodiversity of catalytic super-Brownian motion. Ann. Appl. Probab. To appear.
    • (2000) Ann. Appl. Probab.
    • Fleischmann, K.1    Klenke, A.2
  • 19
    • 21844503686 scopus 로고
    • A new approach to the single point catalytic super-Brownian motion
    • FLEISCHMANN, K. and LE GALL, J.-F. (1995). A new approach to the single point catalytic super-Brownian motion. Probab. Theory Related Fields 102 63-82.
    • (1995) Probab. Theory Related Fields , vol.102 , pp. 63-82
    • Fleischmann, K.1    Le Gall, J.-F.2
  • 20
    • 0031527604 scopus 로고    scopus 로고
    • A super-Brownian motion with a locally infinite catalytic mass
    • FLEISCHMANN, K. and MUELLER, C. (1997). A super-Brownian motion with a locally infinite catalytic mass. Probab. Theory Related Fields 107 325-357.
    • (1997) Probab. Theory Related Fields , vol.107 , pp. 325-357
    • Fleischmann, K.1    Mueller, C.2
  • 21
    • 0002050211 scopus 로고    scopus 로고
    • Finite time extinction of catalytic branching processes
    • Stochastic Models. A Conference in Honour of Donald A. Dawson (L. G. Gorostiza and B. G. Ivanoff, eds.) Providence, RI
    • FLEISCHMANN, K. and MUELLER, C. (2000). Finite time extinction of catalytic branching processes. In Stochastic Models. A Conference in Honour of Donald A. Dawson (L. G. Gorostiza and B. G. Ivanoff, eds.) 125-139. Amer. Math. Soc., Providence, RI.
    • (2000) Amer. Math. Soc. , pp. 125-139
    • Fleischmann, K.1    Mueller, C.2
  • 22
    • 0002127532 scopus 로고
    • Sample function behavior of increasing processes with stationary, independent increments
    • FRISTEDT, B. E. (1967). Sample function behavior of increasing processes with stationary, independent increments. Pacific J. Math. 21 21-33.
    • (1967) Pacific J. Math. , vol.21 , pp. 21-33
    • Fristedt, B.E.1
  • 24
    • 0001150074 scopus 로고    scopus 로고
    • Free energy and dissipation rate for reaction diffusion processes of electrically charged species
    • GLITZKY, A., GRÖCER, K. and HÜNLICH, R. (1996). Free energy and dissipation rate for reaction diffusion processes of electrically charged species. Appl. Anal. 60 201-217.
    • (1996) Appl. Anal. , vol.60 , pp. 201-217
    • Glitzky, A.1    Gröger, K.2    Hünlich, R.3
  • 25
    • 0002133811 scopus 로고    scopus 로고
    • A review on spatial catalytic branching
    • Stochastic Models. A Conference in Honour of Donald A. Dawson (L. G. Gorostiza and B. G. Ivanoff, eds.) Providence, RI
    • KLENKE, A. (2000). A review on spatial catalytic branching. In Stochastic Models. A Conference in Honour of Donald A. Dawson (L. G. Gorostiza and B. G. Ivanoff, eds.) 245-263. Amer. Math. Soc., Providence, RI.
    • (2000) Amer. Math. Soc. , pp. 245-263
    • Klenke, A.1
  • 26
    • 0000535030 scopus 로고
    • Stochastic partial differential equations for some measure-valued diffusions
    • KONNO, N. and SHIGA, T. (1988). Stochastic partial differential equations for some measure-valued diffusions. Probab. Theory Related Fields 79 201-225.
    • (1988) Probab. Theory Related Fields , vol.79 , pp. 201-225
    • Konno, N.1    Shiga, T.2
  • 27
    • 36849109104 scopus 로고
    • Local structures in chemical reactions with heterogeneous catalysis
    • ORTOLEVA, P. and ROSS, J. (1972). Local structures in chemical reactions with heterogeneous catalysis. J. Chemical Phys. 56 4397-4400.
    • (1972) J. Chemical Phys. , vol.56 , pp. 4397-4400
    • Ortoleva, P.1    Ross, J.2
  • 28
    • 0024077125 scopus 로고
    • Aldolase exists in both the fluid and solid phases of cytoplasm
    • PAGLIARO, L. and TAYLOR, D. L. (1988). Aldolase exists in both the fluid and solid phases of cytoplasm. J. Cell Biology 107 981-999.
    • (1988) J. Cell Biology , vol.107 , pp. 981-999
    • Pagliaro, L.1    Taylor, D.L.2
  • 29
    • 0000833829 scopus 로고
    • On the martingale problem for interactive measure-valued branching diffusions
    • PERKINS, E. A. (1995). On the martingale problem for interactive measure-valued branching diffusions. Mem. Amer. Math. Soc. 549.
    • (1995) Mem. Amer. Math. Soc. , vol.549
    • Perkins, E.A.1
  • 31
    • 0001359823 scopus 로고
    • Infinite-dimensional stochastic differential equations and their applications
    • SHIGA, T. and SHIMIZU, A. (1980). Infinite-dimensional stochastic differential equations and their applications. J. Math. Kyoto Univ. 20 395-416.
    • (1980) J. Math. Kyoto Univ. , vol.20 , pp. 395-416
    • Shiga, T.1    Shimizu, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.