2002/03/31 by Yves Le Jan, Olivier Raimond · 1 citation
Mathematics · #math.PR #msc:60H10 #msc:60H40 #msc:60G51 #msc:76F05
paper · pdf · doi:10.1214/009117904000000207
published as Annals of Probability 2004, Vol. 32, No. 2, 1247-1315 · Published at http://dx.doi.org/10.1214/009117904000000207 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2019/07/23 · arxiv updated 2019/07/24
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.