论文信息 - Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions

Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions

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.

Andrew M. Stuart | Jonathan C. Mattingly | A. Stuart

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