On the Poisson equation and diffusion approximation. I

被引：2

作者：

Pardoux, E

Veretennikov, AY

机构：

[1] Univ Aix Marseille 1, Ctr Math & Informat, F-13453 Marseille 13, France

[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 101447, Russia

来源：

ANNALS OF PROBABILITY | 2001年 / 29卷 / 03期

关键词：

Poisson equation; polynomial recurrence; diffusion approximation;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1061 / 1085

页数：25

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