The Annals of Probability

On the Poisson equation and diffusion approximation 3

E. Pardoux and A. Yu. Veretennikov

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Abstract

We study the Poisson equation Lu+f=0 in ℝd, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is ergodic. The equation is understood in a weak sense. Our results are then applied to diffusion approximation.

Article information

Source
Ann. Probab., Volume 33, Number 3 (2005), 1111-1133.

Dates
First available in Project Euclid: 6 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1115386720

Digital Object Identifier
doi:10.1214/009117905000000062

Mathematical Reviews number (MathSciNet)
MR2135314

Zentralblatt MATH identifier
1071.60022

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60J60: Diffusion processes [See also 58J65] 35J70: Degenerate elliptic equations

Keywords
Poisson equation degenerate diffusion diffusion approximation

Citation

Pardoux, E.; Veretennikov, A. Yu. On the Poisson equation and diffusion approximation 3. Ann. Probab. 33 (2005), no. 3, 1111--1133. doi:10.1214/009117905000000062. https://projecteuclid.org/euclid.aop/1115386720


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