Particle representations for a class of nonlinear SPDEs

Stochastic Processes and their Applications

Volumn 83, Issue 1, 1999, Pages 103-126

  Kurtz, Thomas G ^a   Xiong, Jie ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

Author keywords

35R60; 60G09; 60H15; 60K35; Exchangeability; McKean Vlasov equations; Particle representations; Stochastic partial differential equations; Systems of stochastic differential equations

Indexed keywords

EID: 0000273833     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00024-1     Document Type: Article

References (21)

1. Bernard P., Talay D., Tubaro L. Rate of convergence for the Kolmogorov equation with variable coefficients. Math. Comput. 63:1994;555-587.
2. Chiang T., Kallianpur G., Sundar P. Propagation of chaos and McKean-Vlasov equation in duals of nuclear spaces. Appl. Math. and Optim. 24:1991;55-83.
3. Crisan D., Lyons T. Nonlinear filtering and measure-valued processes. Probab. Theory Related Fields. 109:1997;217-244.
4. Crisan, D., Gaines, J., Lyons, T., 1998. Convergence of a branching particle method to the solution of the Zakai equation. SIAM J. Appl. Math. 58, 1568-1590.
5. Dawson D.A., Vaillancourt J. Stochastic McKean-Vlasov equations. NoDEA Nonlinear Differential Equations. Appl. 2:1995;199-229.
6. Del Moral P. Non-linear filtering using random particles. Theory Probab. Appl. 40:1995;690-701.
7. Ethier, S.N., Kurtz, T.G., 1986. Markov Processes: Characterization and Convergence. Wiley, New York.
8. Florchinger, P., Le Gland, F., 1992. Particle approximations for first order stochastic partial differential equations. Applied Stochastic Analysis. New Brunswick, NJ, 1991, Lecture Notes in Control and Inform. Sci., vol. 177. Springer, Berlin, pp. 121-133.
9. Graham C. Nonlinear Ito-Skorohod equations and martingale problem with discrete jump sets. Stochastic Process. Appl. 40:1992;69-82.
10. Hitsuda M., Mitoma I. Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions. J. Multivariate Anal. 19:1986;311-328.
11. Kallianpur G., Xiong J. Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures. Appl. Math. Optim. 30:1994;175-201.
12. Kallianpur, G., Xiong, J., 1995. Stochastic differential equations in infinite dimensional spaces. IMS Lecture Notes-Monograph Series, vol. 26. Institute of Mathematical Statistics.
13. Kotelenez P. A class of quasilinear stochastic partial differential equation of McKean-Vlasov type with mass conservation. Probab. Theory Related Fields. 102:1995;159-188.
14. Kotelenez, P., Kurtz, T.G., 1999., in preparation.
15. Kurtz, T.G., Protter, P., 1996. Weak convergence of stochastic integrals and differential equations. II. Infinite-dimensional case. Probabilistic Models for Nonlinear Partial Differential Equations, Lecture Notes in Math., vol. 1627. Springer, Berlin, pp. 197-285.
16. McKean, H.P., 1967. Propagation of chaos for a class of non-linear parabolic equations. Lecture Series in Differential Equations, vol. 2, pp. 177-194.
17. Méléard, S., 1996. Asymptotic behavior of some interacting particle systems, McKean-Vlasov and Boltzmann models. Probabilistic Models for Nonlinear Partial Differential Equations, Lecture Notes in Math., vol. 1627, pp. 42-95.
18. Morien P.L. Propagation of chaos and fluctuations for a system of weakly interacting white noise driven parabolic SPDE's. Stochastics Stochastics Rep. 58:1996;1-43.
19. Sowers R.B. Intermittency-type estimates for some nondegenerate SPDE's. Ann. Probab. 23:1995;1853-1874.
20. Xiong, J., 1999. A nonlinear differential equation associated with a class of interacting diffusion systems, submitted for publication.
21. Yamada T., Watanabe S. On the uniqueness of stochastic differential equations. J. Math. Kyoto Univ. 11:1971;155-167.