Stochastic Lagrangian flows on some compact manifolds

Abstract

We investigate ponctual as well as L ² 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 construction and on the drift properties.

Keywords:

• stochastic analysis
• diffusion process
• hydrodynamics

AMS Classification::

• 58J65
• 60H30
• 60H10

Notes

^1. [email protected]