INTEGRABILITY AND TAIL ESTIMATES FOR GAUSSIAN ROUGH DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Cass, Thomas; Litterer, Christian; Lyons, Terry
• 署名单位: Imperial College London; University of Oxford
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP821
• 发表日期: 2013
• 页码: 3026-3050
• 关键词: theorem; driven; ergodicity

摘要

We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H > 1/4. We remark on the relevance of such estimates to a number of significant open problems.