Asymptotic Properties of Isotropic Brownian Flows

  • Yves le Jan
Part of the Progress in Probability book series (PRPR, volume 19)

Abstract

Denote by Diff(M) the group of C diffeomorphisms of a Riemannian manifold M. Define a Brownian flow on M as a Diff(M)-valued process Φt, with independent incrementst1, Φt2 ο Φt1 -1, ..., Φt1+1 ο Φti -1 if, t1 < t2 ... < ti). We assume in addition that the increments of the flow are stationarys(law) ~ Φt+s ο Φt -1) and that for any init ial value xM, the one point process Φt(x) is a Brownian motion on M. An analytical characterization of Brownian flows is given in [1].

Keywords

Entropy Manifold Covariance 

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Yves le Jan
    • 1
  1. 1.Laboratoire de Probabilités (CNRS)ParisFrance

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