Open Access
April 2004 Flows, coalescence and noise
Yves Le Jan, Olivier Raimond
Ann. Probab. 32(2): 1247-1315 (April 2004). DOI: 10.1214/009117904000000207


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.


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Yves Le Jan. Olivier Raimond. "Flows, coalescence and noise." Ann. Probab. 32 (2) 1247 - 1315, April 2004.


Published: April 2004
First available in Project Euclid: 18 May 2004

zbMATH: 1065.60066
MathSciNet: MR2060298
Digital Object Identifier: 10.1214/009117904000000207

Primary: 60G51 , 60H10 , 60H40 , 76F05

Keywords: Coalescing flow , Feller convolution semigroup , isotropic Brownian flow , noise , Sobolev flow , Stochastic differential equations , stochastic flow , stochastic flow of kernels , Strong solution

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 2 • April 2004
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