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Self-interacting diffusions. III. Symmetric interactions
Auteur(s)
Raimond, Olivier
Date de parution
2005
In
Annals of Probability
Vol.
5
No
33
De la page
1716
A la page
1759
Résumé
Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to where {W-t} is a Brownian vector field on M and V-x(y) = V(x, y) a smooth function. Let mu(t) = 1/t integral(0)(t) delta X-s ds denote the normalized occupation measure of X-t. We prove that, when V is symmetric, mu(t) converges almost surely to the critical set of a certain nonlinear free energy functional J. Furthermore, J has generically finitely many critical points and mu(t) converges almost surely toward a local minimum of J. Each local minimum has a positive probability to be selected.
Identifiants
Type de publication
journal article
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