Some Particular Self-interacting Diffusions: Ergodic Behavior and Almost Sure Convergence Sébastien Chambeu and Aline Kurtzmann
نویسنده
چکیده
This paper deals with some self-interacting diffusions (Xt, t ≥ 0) living on R. These diffusions are solutions to stochastic differential equations: dXt = dBt − g(t)∇V (Xt − μt)dt, where μt is the mean of the empirical measure of the process X , V is an asymptotically strictly convex potential and g is a given function. We study the ergodic behavior of X and prove that it is strongly related to g. Actually, we show that X is ergodic (in the limit-quotient sense) if and only if μt converges a.s. We also give some conditions (on g and V ) for the almost sure convergence of X .
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Convergence in Distribution of Some Particular Self-interacting Diffusions: the Simulated Annealing Method
The present paper is concerned with some self-interacting diffusions (Xt, t ≥ 0) living on R. These diffusions are solutions to stochastic differential equations: dXt = dBt − g(t)∇V (Xt − μt)dt where μt is the empirical mean of the process X, V is an asymptotically strictly convex potential and g is a given function. The authors have still studied the ergodic behavior of X and proved that it is...
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