On the Poisson equation and diffusion approximation 3

Details On the Poisson equation and diffusion approximation 3 On the Poisson equation and diffusion approximation 3

2005-06-29

arxiv.org/abs/math/0506596v1

Annals of Probability 2005, Vol. 33, No. 3, 1111-1133

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000062 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117905000000062

We study the Poisson equation Lu+f=0 in R^d, 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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