Long-time behavior and coexistence in a mutually catalytic branching model

Annals of Probability

Volumn 26, Issue 3, 1998, Pages 1088-1138

  Dawson, Donald A ^a   Perkins, Edwin A ^b  

^a Flds Inst for Res in Math Sci   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Branching; Coexistence of types; Dual process; Equilibrium distribution; Measure valued processes; Superprocesses

Indexed keywords

EID: 0032393494     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022855746     Document Type: Article

References (24)

1. BARLOW, M. T., EVANS, S. N. and PERKINS, E. A. (1991). Collision local times and measure-valued processes. Canad. J. Math. 43 897-908.
2. DAWSON, D. A. (1977). The critical measure diffusion process. Z. Wahrsch. Verw. Gebiete 40 125-145.
3. DAWSON, D. A. and FLEISCHMANN, K. (1988). Strong clumping of critical space-time branching models in subcritical dimensions. Stochastic Process Appl. 30 193-208.
4. DAWSON, D. A. and FLEISCHMANN, K. (1994). A super-Brownian motion with a single point catalyst. Stochastic Process Appl. 49 3-40.
5. DAWSON, D. A. and FLEISCHMANN, K. (1995). Super-Brownian motions in higher dimensions with absolutely continuous measure states. J. Theoret. Probab. 8 179-206.
6. DAWSON, D. A. and HOCHBERG, K. (1979). The carrying dimension of a stochastic measure diffusion. Ann. Probab. 7 693-703.
7. DAWSON, D. A. and MARCH, P. (1995). Resolvent estimates for Fleming-Viot operators and uniqueness of solutions to related martingale problems. J. Funct. Anal. 132 417-472.
8. DELLACHERIE, C. and MEYER, P. A. (1978). Probabilities and Potential. North-Holland, Amsterdam.
9. DELMAS, J-F. (1996). Super-mouvement Brownien avec catalyse. Stochastics Stochastics Rep. 58 303-347.
10. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
11. GAUTHIER, G. (1997). Multilevel bilinear systems of stochastic differential equations. Stochastic Process. Appl. 67 117-138.
12. IKEDA, N. and WATANABE, S. (1981). Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.
13. LAWLER, G. F. (1991). Intersections of Random Walks. Birkäuser, Boston.
14. LIGGETT, T. M. (1985). Interacting Particle Systems. Springer, New York.
15. MUELLER, C. and PERKINS, E. A. (1997). Extinction for some parabolic stochastic p.d.e.'s on the lattice. Unpublished manuscript.
16. MYTNIK, L. (1997). Uniqueness for a mutually catalytic branching model Probab. Theory Related Fields. To appear.
17. PERKINS, E. A. (1988). A space-time property of a class of measure-valued branching diffusions. Trans. Amer. Math. Soc. 305 743-795.
18. PERKINS, E. A. (1995). On the Martingale Problem for Interactive Measure-valued Branching Diffusions. Mem. Amer. Math. Soc. 115 549.
19. SHIGA, T. (1994). Two contrasting properties of solutions for one-dimensional stochastic partial differential equations. Canad. J. Math. 46 415-437.
20. SHIGA, T. and SHIMIZU, A. (1980). Infinite dimensional stochastic differential equations and their applications. J. Math. Kyoto Univ. 20 395-416.
21. STROOCK, D. W. and VARADHAN, S. R. S. (1979). Multidimensional Diffusion Processes. Springer, Berlin.
22. WALSH, J. B. (1986). An introduction to stochastic partial differential equations. Ecole d'été de Probabilités Saint-Flour XIV 1984. Lecture Notes in Math. 1180 265-439. Springer, Berlin.
23. WILLIAMS, D. (1991). Probability with Martingales. Cambridge Univ. Press.
24. YOR, M. (1978). Continuité des temps locaux. In Temps Locaux. Astérisque 52-53 17-22.