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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. 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
Related URLs:
URLURL TypeDescription
http://math-mprf.org/journal/articles/id930/PublisherArticle
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9971087
Subject Keywords:geometric ergodicity, stochastic differential equations, Langevin equation, synthetic turbulence, hypoelliptic and degenerate diffusions
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ52
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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