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Ergodicity of self-attracting motion

   
@article{EJP2121,
	author = {Victor Kleptsyn and Aline Kurtzmann},
	title = {Ergodicity of self-attracting motion},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {self-attracting diffusion ; dynamical system ; free energy},
	abstract = { 
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.
},
	pages = {no. 50, 1-37},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2121},    
        url = {http://ejp.ejpecp.org/article/view/2121}}