Rate of convergence of some self-attracting diffusions
نویسندگان
چکیده
منابع مشابه
1 Ju l 2 00 9 Self - interacting diffusions IV : Rate of convergence ∗
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure μt of the process. The asymptotics of μt is governed by a deterministic dynamical system and under certain conditions (μt) converges almost surely towards a deterministic measure μ ∗ (see Benäım, Ledoux, Raimond...
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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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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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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...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2004
ISSN: 0304-4149
DOI: 10.1016/j.spa.2003.10.012