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Preprints, Working Papers, ... Year : 2011

Self-stabilizing processes in multi-wells landscape in $\bRb^d$ - Invariant probabilities

Julian Tugaut

Abstract

The aim of this work is to analyse the stationary measures for a particular class of non-markovian diffusions: the self-stabilizing processes. All the trajectories of such a process attract each other. This permits to exhibit a non-uniqueness of the stationary measures in the one-dimensional case, see "Non uniqueness of stationary measures for self-stabilizing processes" [Herrmann, Tugaut, 2010]. In this paper, the extension to general multi-wells lansdcape in general dimension is provided. Moreover, the method for investigating this problem is different and needs less assumptions. The small-noise limit behavior of the invariant probabilities is also given.
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Dates and versions

hal-00627901 , version 1 (29-09-2011)

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  • HAL Id : hal-00627901 , version 1

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Julian Tugaut. Self-stabilizing processes in multi-wells landscape in $\bRb^d$ - Invariant probabilities. 2011. ⟨hal-00627901⟩
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