Flows, coalescence and noise

Le Jan, Yves ; Raimond, Olivier

Ann. Probab., Tome 32 (2004) no. 1A, p. 1247-1315 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2004-04-14
Classification:  Stochastic differential equations,  strong solution,  stochastic flow,  stochastic flow of kernels,  Sobolev flow,  isotropic Brownian flow,  coalescing flow,  noise,  Feller convolution semigroup,  60H10,  60H40,  60G51,  76F05