Convergence in Distribution of Some Particular Self-interacting Diffusions: the Simulated Annealing Method
نویسنده
چکیده
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 strongly related to g. We go further and give necessary and sufficient conditions (for small g’s) in order that X converges in probability to X∞ (which is related to the global minima of V ).
منابع مشابه
Convergence in Distribution of Some Self-interacting Diffusions: the Simulated Annealing Method
We study some self-interacting diffusions living on R solutions to: 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, not increasing too fast to the infinity or constant. The authors have already proved that the ergodic behavior of X is strongly related to g. We go further and, using the s...
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