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Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions

Mattingly, J. C. and Stuart, A. M. (2002) Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions. Markov Processes And Related Fields, 8 (2). pp. 199-214. ISSN 1024-2953.

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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.

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Additional Information:© 2002 Markov Processes and Related Fields. Supported by the National Science Foundation under grant DMS-9971087. We would like to thank Des Higham, and Wilhelm Huisinga for helpful input.
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Subject Keywords:geometric ergodicity, stochastic differential equations, Langevin equation, synthetic turbulence, hypoelliptic and degenerate diffusions
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Andrew StuartJ52
Issue or Number:2
Record Number:CaltechAUTHORS:20170613-125012320
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78164
Deposited By: Tony Diaz
Deposited On:13 Jun 2017 20:02
Last Modified:03 Oct 2019 18:06

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