On poisson equation and diffusion approximation 21

• 成果类型: Article
• 署名作者: Pardoux, É; Veretennikov, Y
• 署名单位: Aix-Marseille Universite; University of Leeds; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 1166-1192
• 关键词: differential-equations

摘要

Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of an invariant diffusion density with respect to a parameter. The second establishes a similar smoothness of the solution of the Poisson equation in R-d. The third one states a diffusion approximation result, or in other words an averaging of singularly perturbed diffusion for fully coupled SDE systems or SDE systems with complete dependence..