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July 2001 On the Poisson Equation and Diffusion Approximation. I
E. Pardoux, Yu. Veretennikov
Ann. Probab. 29(3): 1061-1085 (July 2001). DOI: 10.1214/aop/1015345596

Abstract

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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E. Pardoux. Yu. Veretennikov. "On the Poisson Equation and Diffusion Approximation. I." Ann. Probab. 29 (3) 1061 - 1085, July 2001. https://doi.org/10.1214/aop/1015345596

Information

Published: July 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1029.60053
MathSciNet: MR1872736
Digital Object Identifier: 10.1214/aop/1015345596

Subjects:
Primary: 35J15 , 60H30 , 60J45 , 60J60

Keywords: diffusion approximation , Poisson equation , polynomial recurrence

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 3 • July 2001
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