Particle representations for a class of nonlinear SPDEs
作者： Thomas G. Kurtz , Jie Xiong
DOI: 10.1016/S0304-4149(99)00024-1
关键词: Partial differential equation 、 Stochastic partial differential equation 、 Stochastic process 、 Nonlinear system 、 Lebesgue measure 、 Mathematical analysis 、 Empirical measure 、 Probability measure 、 Mathematics 、 Class (set theory) 、 Applied mathematics
摘要: An innite system of stochastic dierential equations for the locations and weights a collection particles is considered. The interact through their weighted empirical measure, V, V shown to be unique solution nonlinear partial equation (SPDE). Conditions are given under which measure has an L2-density with respect Lebesgue measure. c 1999 Elsevier Science B.V. All rights reserved. MSC: 60H15; 60K35; 35R60; 60G09
elsevier.com
sci-hub.se 参考文章(21)
T.S. Chiang, G. Kallianpur, P. Sundar, Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces. Technical report ,(1990)
Toshio Yamada, Shinzo Watanabe, On the uniqueness of solutions of stochastic differential equations Journal of Mathematics of Kyoto University. ,vol. 11, pp. 155- 167 ,(1971) , 10.1215/KJM/1250523691
Thomas G. Kurtz, Philip E. Protter, Weak convergence of stochastic integrals and differential equations Lecture Notes in Mathematics. pp. 1- 41 ,(1996) , 10.1007/BFB0093176
Jie Xiong, Gopinath Kallianpur, Stochastic Differential Equations in Infinite Dimensional Spaces ,(1995)
Carl Graham, McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets Stochastic Processes and their Applications. ,vol. 40, pp. 69- 82 ,(1992) , 10.1016/0304-4149(92)90138-G
Dan Crisan, Terry Lyons, Nonlinear filtering and measure-valued processes Probability Theory and Related Fields. ,vol. 109, pp. 217- 244 ,(1997) , 10.1007/S004400050131
Pierre Bernard, Denis Talay, Luciano Tubaro, Rate of convergence of a stochastic particle method for the Kolmogorov equation with variable coefficients Mathematics of Computation. ,vol. 63, pp. 555- 587 ,(1994) , 10.2307/2153283
T. S. Chiang, G. Kallianpur, P. Sundar, Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces Applied Mathematics & Optimization. ,vol. 24, pp. 55- 83 ,(1991) , 10.1007/BF01447735
Donald Dawson, Jean Vaillancourt, Stochastic McKean-Vlasov equations Nodea-nonlinear Differential Equations and Applications. ,vol. 2, pp. 199- 229 ,(1995) , 10.1007/BF01295311
Dan Crisan, Jessica Gaines, Terry Lyons, Convergence of a Branching Particle Method to the Solution of the Zakai Equation SIAM Journal on Applied Mathematics. ,vol. 58, pp. 1568- 1590 ,(1998) , 10.1137/S0036139996307371