The Annals of Probability

On the Poisson Equation and Diffusion Approximation. I

E. Pardoux and Yu. Veretennikov

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A Poisson equation in $\mathbb{R}^d$ 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 usingthe method of corrector; the solution of a Poisson equation serves as a corrector.

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Ann. Probab., Volume 29, Number 3 (2001), 1061-1085.

First available in Project Euclid: 5 March 2002

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Primary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J60: Diffusion processes [See also 58J65] 35J15: Second-order elliptic equations

Poisson equation polynomial recurrence diffusion approximation


Pardoux, E.; Veretennikov, Yu. On the Poisson Equation and Diffusion Approximation. I. Ann. Probab. 29 (2001), no. 3, 1061--1085. doi:10.1214/aop/1015345596.

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