| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Probability
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| Title: |
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Ergodicity of self-attracting motion |
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| Author(s): |
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Victor Kleptsyn ( ) 1, Aline Kurtzmann () 2 |
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| Laboratory: |
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| Abstract: |
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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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| Fulltext language: |
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English |
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| Production date: |
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2010-03-31 |
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| Comment: |
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34 pages |
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| Project(s), collaboration(s): |
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Victor Kleptsyn, Aline Kurtzmann |
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