Ergodicity of self-attracting motion

Victor Kleptsyn (Université de Rennes 1)
Aline Kurtzmann (Université de Lorraine)


We study the asymptotic behaviour of a class of self-attracting motions on $\mathbb{R}^d$. We prove the decrease of the free energy related to the system and mix it together with stochastic approximation methods. We finally obtain the (limit-quotient) ergodicity of the self-attracting diffusion with a speed of convergence.

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Pages: 1-37

Publication Date: June 29, 2012

DOI: 10.1214/EJP.v17-2121


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