On the spatial asymptotic behavior of stochastic flows in Euclidean space

• 成果类型: Article
• 署名作者: Imkeller, P; Scheutzow, M
• 署名单位: Humboldt University of Berlin; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 109-129
• 关键词: multiplicative ergodic-theory; differential-equations

摘要

We study asymptotic growth rates of stochastic flows on Rd and their derivatives with respect to the spatial parameter under Lipschitz conditions on the local characteristics of the generating semimartingales. In a first step these conditions are seen to imply moment inequalities for the flow phi of the form E sup \phi(0t)(x) - phi(0t)(y)\(p) less than or equal to \x - y\p exp(cp(2)) for all p greater than or equal to 1. 0 less than or equal to t less than or equal to T In a second step we deduce the growth rates from an integrated version of these moment inequalities, using the continuity lemma of Garsia, Rodemich and Rumsey. We provide two examples to show that our results are sharp.