On the Poisson equation and diffusion approximation. I
成果类型：
Article
署名作者：
Pardoux, E; Veretennikov, AY
署名单位：
Aix-Marseille Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2001
页码：
1061-1085
关键词：
摘要：
A Poisson equation in R-d for the elliptic operator corresponding to an ergodic diffusion process is considered. Existence and uniqueness of its solution in Sobolev classes of functions is established along with the bounds for its growth. This result is used to study a diffusion approximation for two-scaled diffusion processes using the method of corrector; the solution of a Poisson equation serves as a corrector.