Flows, coalescence and noise

Yves Le Jan, Olivier Raimond

Research output: Contribution to journalArticlepeer-review

Abstract

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. Stochastic differential equations, strong solution, stochastic flow, stochastic flow of kernels, Sobolev flow, isotropic Brownian flow, coalescing flow, noise, Feller convolution semigroup.

Original languageEnglish (US)
Pages (from-to)1247-1315
Number of pages69
JournalAnnals of Probability
Volume32
Issue number2
DOIs
StatePublished - Apr 2004

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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