On the Poisson equation and diffusion approximation 3

2005/05/01 by Étienne Pardoux, E. Pardoux, A. Yu. Veretennikov · 8 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:35J70 #msc:60F17 #msc:60J60

paper · pdf · doi:10.1214/009117905000000062

published as Annals of Probability 2005, Vol. 33, No. 3, 1111-1133 · Published at http://dx.doi.org/10.1214/009117905000000062 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/05/01 · arxiv created 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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