Ergodic theory for sdes with extrinsic memory

• 成果类型: Article
• 署名作者: Hairer, M.; Ohashi, A.
• 署名单位: University of Warwick; Universidade Estadual de Campinas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001141
• 发表日期: 2007
• 页码: 1950-1977
• 关键词: differential-equations driven; fractional brownian motions; rough paths

摘要

We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a class of non-Markovian systems. They allow us to obtain a criteria for ergodicity which is similar in nature to the Doob-Khas'minskii theorem. The second part of this article shows how it is possible to apply these results to the case of stochastic differential equations driven by fractional Brownian motion. It follows that under a nondegeneracy condition on the noise, such equations admit a unique adapted stationary solution.