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

Julian Tugaut (1)

1 Universität Bielefeld = Bielefeld University

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.

Mots clés: Self-interacting diffusion; Free-energy; McKean-Vlasov stochastic differential equations; Stationary measures; Uniqueness problem; Granular media equation

Domaines: Probabilités [math.PR]

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