Flows, coalescence and noise

• 成果类型: Article
• 署名作者: Le Jan, Y; Raimond, O
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000207
• 发表日期: 2004
• 页码: 1247-1315
• 关键词: diffeomorphism group; brownian-motion

摘要

We are interested in stationary fluid random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE can be obtained by filtering a coalescing motion with respect to a subnoise containing the Gaussian part of its noise. Thus, the coalescing motion cannot be described by a white noise.