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Summary: STOCHASTIC LAGRANGIAN FLOWS ON SOME COMPACT
MANIFOLDS
MARC ARNAUDON AND ANA BELA CRUZEIRO
Abstract. We investigate ponctual as well as L2 distances of some stochastic
processes with values in the group of homeomorphisms of a compact manifold
including processes modelling time evolution of fluids. These processes are
associated with operators of the form Laplace-Beltrami plus a first order term.
Several constructions are presented, in particular via coupling methods, the
corresponding behaviour of the distance depending on the constuction and on
the drift properties.
Contents
1. Introduction 1
2. Preliminaries 2
3. The distance between two particles: a coupling approach 3
4. The distance between two particles: a stochastic flow approach 12
References 14
1. Introduction
The Navier-Stokes system
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