The Annals of Probability

On the Poisson equation and diffusion approximation 3

E. Pardoux and A. Yu. Veretennikov

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

First available in Project Euclid: 6 May 2005

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Zentralblatt MATH identifier

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

Poisson equation degenerate diffusion diffusion approximation


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.

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