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Published February 24, 2016 | Submitted
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Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums


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.

Additional Information

(Submitted on 23 Oct 2007 (v1), last revised 10 Apr 2008 (this version, v4). February 16, 2013.

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Submitted - 0710.4259.pdf


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