Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions

J.C. Mattingly, A.M. Stuart

2002, v.8, №2, 199-214

ABSTRACT

Two degenerate SDEs arising in statistical physics are studied. The first is a Langevin equation with state-dependent noise and damping. The second is the equation of motion for a particle obeying Stokes' law in a Gaussian random field; this field is chosen to mimic certain features of turbulence. Both equations are hypo-elliptic and smoothness of probability densities may be established. By developing appropriate Lyapunov functions and by studying the necessary control problems, geometric ergodicity is proved.

Keywords: geometric ergodicity,stochastic differential equations,Langevin equation,synthetic turbulence,hypoelliptic and degenerate diffusions

COMMENTS

Please log in or register to leave a comment


There are no comments yet