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. https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320
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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.
Item Type: | Article | ||||||
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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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Issue or Number: | 2 | ||||||
Record Number: | CaltechAUTHORS:20170613-125012320 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 78164 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 13 Jun 2017 20:02 | ||||||
Last Modified: | 03 Oct 2019 18:06 |
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