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May 2005 On the Poisson equation and diffusion approximation 3
E. Pardoux, A. Yu. Veretennikov
Ann. Probab. 33(3): 1111-1133 (May 2005). DOI: 10.1214/009117905000000062

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.

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E. Pardoux. A. Yu. Veretennikov. "On the Poisson equation and diffusion approximation 3." Ann. Probab. 33 (3) 1111 - 1133, May 2005. https://doi.org/10.1214/009117905000000062

Information

Published: May 2005
First available in Project Euclid: 6 May 2005

zbMATH: 1071.60022
MathSciNet: MR2135314
Digital Object Identifier: 10.1214/009117905000000062

Subjects:
Primary: 35J70 , 60F17 , 60J60

Keywords: degenerate diffusion , diffusion approximation , Poisson equation

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 3 • May 2005
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