Homogenization for stochastic partial differential equations derived from nonlinear filterings with feedback. (English) Zbl 1084.60040

Ichihara, Naoyuki

J. Math. Soc. Japan 57, No. 2, 593-603 (2005).

Summary: We discuss the homogenization of stochastic partial differential equations whose coefficients are rapidly oscillating and are perturbed by a diffusion process. Such class of equations appear in nonlinear filtering problems with feedback. We specify the constant coefficients of the limit equation. The constants are essentially different from the case where the coefficients do not contain perturbed factors.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations
93C20	Control/observation systems governed by partial differential equations
49J45	Methods involving semicontinuity and convergence; relaxation