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Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums

Bou-Rabee, Nawaf and Owhadi, Houman (2013) Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums. . http://resolver.caltech.edu/CaltechAUTHORS:20160224-103320707

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Abstract

This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with non-degenerate diffusion component (but that may be applied to a single degree of freedom of the system). The geometric conditions are the approximate controllability of the process the fact that there exists a point in the phase space where the interior of the image of a point via a secondarily randomized version of the driving noise is non void. The paper applies the method to prove ergodicity of a sliding disk governed by Langevin-type equations (a simple stochastic rigid body system). The paper shows that a key feature of this Langevin process is that even though the diffusion and drift matrices associated to the momentums are degenerate, the system is still at uniform temperature.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/0710.4259arXivDiscussion Paper
ORCID:
AuthorORCID
Owhadi, Houman0000-0002-5677-1600
Additional Information:(Submitted on 23 Oct 2007 (v1), last revised 10 Apr 2008 (this version, v4). February 16, 2013.
Record Number:CaltechAUTHORS:20160224-103320707
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160224-103320707
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64731
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 19:11
Last Modified:11 Jul 2017 00:22

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