Publications [#10329] of Jonathan C. Mattingly

Papers Published

1. Mattingly, J. C. and Stuart, A. M., Geometric ergodicity of some hypo-elliptic diffusions for particle motions, Markov Process. Related Fields, vol. 8 no. 2 (2002), pp. 199--214 (Inhomogeneous random systems (Cergy-Pontoise, 2001).)
   (last updated on 2004/07/13)

   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.