Asymptotic Properties of Isotropic Brownian Flows
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 increments (Φt1, Φt2 ο Φt1 -1, ..., Φt1+1 ο Φti -1 if, t1 < t2 ... < ti). We assume in addition that the increments of the flow are stationary (Φs(law) ~ Φt+s ο Φt -1) and that for any init ial value x ∈ M, the one point process Φt(x) is a Brownian motion on M. An analytical characterization of Brownian flows is given in .
KeywordsBrownian Motion Asymptotic Property Dirichlet Form Curvature Vector Part Formula
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