| Contents |
| Let $(M, \mathcal{F})$ be a compact Riemannian foliated
manifold.
We consider a family of compatible Feller
semigroups in $C(M^n)$ associated to laws of the $n$-point
motion.
Under some assumptions (Le Jan and Raimond, Annals of Prob. 2004)
there
exists a stochastic flow of measurable mappings in $M$. We study the
degeneracy of these semigroups such that the
flow of mappings is
foliated, i.e. each trajectory lays in a single leaf of the foliation a.s,
hence creating a geometrical obstruction for coalescence of trajectories in
different
leaves. As an application, an
averaging principle is proved for a first order perturbation transversal to the
leaves. Estimates for the rate of
convergence are calculated. |
|