On the Poisson equation and diffusion approximation 3

• 成果类型: Article
• 署名作者: Pardoux, E; Veretennikov, AY
• 署名单位: Aix-Marseille Universite; University of Leeds; Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000062
• 发表日期: 2005
• 页码: 1111-1133
• 关键词: operators

摘要

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.