Math @ Duke

Publications [#243838] of Jonathan C. Mattingly
Papers Published
 Mattingly, JC; Stuart, AM, Geometric ergodicity of some hypoelliptic diffusions for particle motions,
Markov Processes and Related Fields, vol. 8 no. 2
(2002),
pp. 199214, ISSN 10242953 (Inhomogeneous random systems (CergyPontoise,
2001).) [MR2003g:60101], [pdf]
(last updated on 2018/02/21)
Abstract: Two degenerate SDEs arising in statistical
physics are studied.
The first is a Langevin equation with
statedependent 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
hypoelliptic and smoothness
of probability densities may be established.
By developing
appropriate Lyapunov functions and by
studying the necessary
control problems, geometric ergodicity is proved.


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