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Convergence in distribution of some self-interacting diffusions
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نویسنده
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kurtzmann a.
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منبع
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journal of probability and statistics - 2014 - دوره : 2014 - شماره : 0
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چکیده
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The present paper is concerned with some self-interacting diffusions (xt,t ≥ 0) living on d. these diffusions are solutions to stochastic differential equations: dxt = dbt - g (t) δ v (xt - μ ̄t) dt,where μ̄ t is the empirical mean of the process x,v is an asymptotically strictly convex potential,and g is a given positive function. we study the asymptotic behaviour of x for three different families of functions g. if g t = k log t with k small enough,then the process x converges in distribution towards the global minima of v,whereas if t g (t) → c ] 0,+ ∞ ] or if g (t) → g(∞) ∈ [0,+ ∞ [,then x converges in distribution if and only if ∫ xe- 2v(x) dx = 0. © 2014 aline kurtzmann.
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آدرس
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université de lorraine,institut elie cartan lorraine,umr 7502 cnrs, France
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Authors
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