Flows, coalescence and noise

Details Flows, coalescence and noise Flows, coalescence and noise

2002-03-21

arxiv.org/abs/math/0203221v5

Annals of Probability 2004, Vol. 32, No. 2, 1247-1315

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000207 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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