{
  "id": "1306.0123",
  "version": "v1",
  "published": "2013-06-01T15:30:15.000Z",
  "updated": "2013-06-01T15:30:15.000Z",
  "title": "Degenerate semigroups and stochastic flows of mappings in foliated manifolds",
  "authors": [
    "Paulo Henrique P da Costa",
    "Paulo R. Ruffino"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "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, \\cite{Le Jan-Raimond}) 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-01T15:30:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30",
      "57C12"
    ],
    "keywords": [
      "stochastic flow",
      "degenerate semigroups",
      "first order perturbation transversal",
      "compact riemannian foliated manifold",
      "single leaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0123D"
    }
  }
}