Ergodicity of stochastic differential equations driven by fractional Brownian motion

• 成果类型: Article
• 署名作者: Hairer, M
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000892
• 发表日期: 2005
• 页码: 703-758
• 关键词: systems; pde

摘要

We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H is an element of (0, 1). A general framework is constructed to make precise the notions of invariant measure and stationary state for such a system. We then prove under rather weak dissipativity conditions that such an SIDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the stationary one is (at least) algebraic. A lower bound on the exponent is also given.