Math @ Duke
Publications [#10329] of Jonathan C. Mattingly
- 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
pp. 199--214 (Inhomogeneous random systems (Cergy-Pontoise,
2001).) [MR2003g:60101], [pdf]
(last updated on 2004/07/13)
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
of turbulence. Both equations are
hypo-elliptic and smoothness
of probability densities may be established.
appropriate Lyapunov functions and by
studying the necessary
control problems, geometric ergodicity is proved.
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