Boundedness and convergence of some self-attracting diffusions |
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| Authors: | Samuel Herrmann Bernard Roynette |
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| Affiliation: | (1) Institut de Mathématiques Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvre-lès-Nancy Cedex, France (e-mail: {Samuel.Herrmann@, Bernard.Roynette}@iecn.u-nancy.fr), FR |
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| Abstract: | We consider some self-attracting diffusions and study the behaviour of their paths when time tends to infinity. We prove that, in case the interaction is nonlocal, the paths are bounded a.s. even if they don't converge. Otherwise, we generalize the convergence result of M. Cranston and Y. Le Jan. Received: 5 March 2001 / Revised version: 3 June 2002 / Published online: 2 December 2002 Mathematics Subject Classification (2000): 60G17, 60J60, 60K35 |
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