Spatial estimates for stochastic flows in Euclidean space

• 成果类型: Article
• 署名作者: Mohammed, SEA; Scheutzow, MKR
• 署名单位: Southern Illinois University System; Southern Illinois University; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 56-77
• 关键词: ordinary differential-equations; exponents

摘要

We study the behavior for large \x\ of Kunita-type stochastic flows phi(t, omega, x) on R-d, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large \x\, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.