Collision local times, historical stochastic calculus, and competing superprocesses

Electronic Journal of Probability

Volumn 3, Issue , 1998, Pages

  Evans, Steven N ^a   Perkins, Edwin A ^a  

^a NONE

Author keywords

Historical process; Interaction; Local time; Martingale measure; Measure valued Markov branching process; Random measure; Stochastic calculus; Super Brownian motion; Super process

Indexed keywords

EID: 0013067177     PISSN: 10836489     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. R.J. Adler and R. Tribe. Uniqueness of a historical SDE with a singular interaction. J. Theoret. Probab., 1997. In Press.
2. M.T. Barlow, S.N. Evans, and E.A. Perkins. Collision local times and measure-valued processes. Canad. J. Math., 43:897-938, 1991.
3. B. Bolker and S.W. Pacala. Using moment equations to understand stochastically driven spatial pattern formation in ecological systems. Theoret. Popul. Biol., 1997. In Press.
4. B. Bolker, S.W. Pacala, and S.A. Levin. Moment methods for stochastic processes in continuous space and time. In U. Dieckmann and J. Metz, editors, Low-Dimensional Dynamics of Spatial Ecological Systems, 1997. In Press.
5. D.A. Dawson. Measure-valued Markov processes. In Ecole d'Eté de Probabilités de Saint-Flour XXI - 1991, volume 1541 of Lecture Notes in Math., pages 1-260. Springer, Berlin, 1993.
6. D.A. Dawson and K. Fleischmann. Longtime behavior of branching processes controlled by branching catalysts. Preprint, 1996.
7. D.A. Dawson and K. Fleischmann. A continuous super-Brownian motion in a super-Brownian medium. J. Theoret. Probab., 1997. In Press.
8. D.A. Dawson and P. March. Resolvent estimates for Fleming-Viot operators and uniqueness of solutions to related martingale problems. J. Funct. Anal., 132:417-472, 1995.
9. D.A. Dawson and E.A. Perkins. Historical processes. Mem. Amer. Math. Soc., 93, 1991.
10. D.A. Dawson and E.A. Perkins. Long-time behaviour and co-existence in a mutually catalytic branching model. Preprint, 1997.
11. C. Dellacherie and P.-A. Meyer. Probabilities and Potential. Number 29 in Mathematics Studies. North-Holland, Amsterdam, 1978.
12. C. Dellacherie and P.-A. Meyer. Probabilities and Potential B. Number 72 in Mathematics Studies. North-Holland, Amsterdam, 1982.
13. E.B. Dynkin. Three classes of infinite dimensional diffusions. J. Funct. Anal., 86:75-110, 1989.
14. E.B. Dynkin. Path processes and historical processes. Probab. Theory Relat. Fields, 90:89-115, 1991.
15. E.B. Dynkin. On regularity of superprocesses. Probab. Theory Relat. Fields, 95:263-281, 1993.
16. N. El-Karoui and S. Roelly. Propriétés de martingales, explosion et représentation de Lévy-Khintchine d'une classe de processus de branchement à valuers mesures. Stoch. Process. Appl., 38:239-266, 1991.
17. A.M. Etheridge and K. Fleischmann. Persistence of a two-dimensional super-Brownian motion in a catalytic medium. Preprint, 1997.
18. S.N. Ethier and T.G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York, 1986.
19. S.N. Evans and E.A. Perkins. Absolute continuity results for superprocesses with some applications. Trans. Amer. Math. Soc., 325:661-681, 1991.
20. S.N. Evans and E.A. Perkins. Measure-valued branching diffusions with singular interactions. Canad. J. Math., 46:120-168, 1994.
21. S.N. Evans and E.A. Perkins. Explicit stochastic integral representations for historical functionals. Ann. Probab., 23:1772-1815, 1995.
22. P.J. Fitzsimmons. Construction and regularity of measure-valued Markov branching processes. Israel J. Math., 64:337-361, 1988.
23. K. Fleischmann and A. Klenke. Smooth density field of catalytic super-Brownian motion. Preprint, 1997.
24. D.N. Hoover and H.J. Keisler. Adapted probability distributions. Trans. Amer. Math. Soc., 286:159-201, 1984.
25. N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam, 1981.
26. M. Lopez. Path properties and convergence of interacting superprocesses. PhD thesis, University of British Columbia, 1996.
27. L. Mytnik. Uniqueness of a competing species model. Preprint, 1997.
28. C. Neuhauser and S.W. Pacala. An explicitly spatial version of the Lotka-Volterra model with interspecific competition. Preprint, 1997.
29. L. Overbeck. Nonlinear superprocesses. Ann. Probab., 24:743-760, 1996.
30. E.A. Perkins. Measure-valued branching diffusion with spatial interactions. Probab. Theory Relat. Fields, 94:189-245, 1992.
31. E.A. Perkins. On the martingale problem for interactive measure-valued branching diffusions. Mem. Amer. Math. Soc., 115, 1995.
32. J.B. Walsh. An introduction to stochastic partial differential equations. In Ecole d'Eté de Probabilités de Saint-Flour XIV - 1984, volume 1180 of Lecture Notes in Math., pages 265-439. Springer, Berlin, 1986.