Numerical solution for a class of SPDEs over bounded domains

作者：Crisan Dan^*; Xiong Jie

来源：Stochastics: An International Journal of Probability and Stochastic Processes , 2014, 86(3): 450-472.

DOI：10.1080/17442508.2013.819510

• stochastic partial differential equations
• interacting particle systems
• diffusions with reflecting boundary
• Kushner-FKK equation
• nonlinear filtering

Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central role in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295-308].

• 出版日期2014
• 单位河北师范大学