Ergodicity of self-attracting motion

Victor Kleptsyn; Aline Kurtzmann

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arXiv · 1005.5632

Ergodicity of self-attracting motion

Victor Kleptsyn·Aline Kurtzmann

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Abstract

The aim of this paper is to study the asymptotic behaviour of a class of self- attracting motions on R^d . Using stochastic approximation methods, these processes have already been studied by Benaïm, Ledoux and Raimond (2002) in a compact setting. We also relate the asymptotic behaviour of the self-attracting Brownian motion to the McKean-Vlasov process that was studied, via the decrease of the free energy, by Carrillo, McCann and Villani (2003). Mixing these methods, we manage to obtain sufficient conditions for the (limit-quotient) ergodicity of the self-attracting diffusion, together with a speed of convergence.

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Victor Kleptsyn, Aline Kurtzmann. 2010-05-31. Ergodicity of self-attracting motion. https://arxiv.org/abs/1005.5632

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