Diffusion limits for a nonlinear density dependent space-time population model

Annals of Probability

Volumn 24, Issue 2, 1996, Pages 639-659

  Blount, Douglas ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Diffusion process; Reaction diffusion model; Stochastic partial differential equation

Indexed keywords

EID: 0030500154     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1039639357     Document Type: Article

References (19)

1. ARNOLD, L. and THEODOSOPULU, M. (1980). Deterministic limit of the stochastic model of chemical reactions with diffusion. Adv. in Appl. Probab. 12 367-379.
2. BLOUNT, D. (1991). Comparison of stochastic and deterministic models of a linear chemical reaction with diffusion. Ann. Probab. 19 1440-1462.
3. BLOUNT, D. (1992). Law of large numbers in the supremum norm for a chemical reaction with diffusion. Ann. Appl. Probab. 2 131-141.
4. BLOUNT, D. (1993). Limit theorems for a sequence of reaction-diffusion systems. Stochastic Process. Appl. 45 193-207.
5. BLOUNT, D. (1994). Density dependent limits for a nonlinear reaction-diffusion model. Ann. Probab. 22 2040-2070.
6. BOLDRIGHINI, C., DE MASI, A. and PELLEGRINOTTI, A. (1992). Nonequilibrium fluctuations in particle systems modeling reaction-diffusion equations. Stochastic Process. Appl. 42 1-30.
7. BURKHOLDER, D. (1973). Distribution function inequalities for martingales. Ann. Probab. 1 19-42.
8. DAWSON, D. (1993). Measure valued Markov processes. Ecole d'Eté de Probabilités de Saint-Flour XX. Lecture Notes in Math. 1541 1-260, Springer, Berlin.
9. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes, Characterization and Convergence. Wiley, New York.
10. EVANS, S. and PERKINS, E. (1994). Measure-valued diffusions with singular interactions. Canad. J. Math. 46 120-168.
11. KONNO, N. and SHIGA, T. (1988). Stochastic partial differential equations for some measure-valued diffusions. Probab. Theory Related Fields 79 201-225.
12. KOTELENEZ, P. (1986). Law of large numbers and center limit theorem for linear chemical reactions with diffusion. Ann. Probab. 14 173-193.
13. KOTELENEZ, P. (1987). Fluctuations near homogeneous states of chemical reactions with diffusion. Adv. in Appl. Probab. 19 352-370.
14. KOTELENEZ, P. (1988). High density limit theorems for nonlinear chemical reactions with diffusion. Probab. Theory Related Fields 78 11-37.
15. KOTELENEZ, P. (1992a). Existence, uniqueness and smoothness for a class of function valued stochastic partial differential equations. Stochastics Stochastics Rep. 41 177-199.
16. KOTELENEZ, P. (1992b). Comparison methods for a class of function valued stochastic partial differential equations. Probab. Theory Related Fields 93 1-19.
17. MUELLER, C. and TRIBE, T. (1995). Stochastic p.d.e.'s arising from the long range contact and long range voter processes. Probab. Theory Related. Fields 102 519-545.
18. TRIBE, R. (1994). The long time behavior of a stochastic P.D.E. Preprint.
19. WALSH, J. (1986). An introduction to stochastic partial differential equations. Lecture Notes in Math. 1180 265-439. Springer, Berlin.