# Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence

Abstract : Self-stabilizing processes are inhomogeneous diffusions in which the law of the process intervenes in the drift. If the external force is the gradient of a convex potential, it has been proved that the process converges toward the unique invariant probability as the time goes to infinity. However, in a previous article, we established that the diffusion may admit several invariant probabilities, provided that the external force derives from a non-convex potential. We here provide results about the limiting values of the family $\left\{\mu_t\,;\,t\geq0\right\}$, $\mu_t$ being the law of the diffusion. Moreover, we establish the weak convergence under an additional hypothesis.
Keywords :
Type de document :
Pré-publication, Document de travail
2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00628086
Contributeur : Julian Tugaut <>
Soumis le : vendredi 10 août 2012 - 08:43:17
Dernière modification le : lundi 13 août 2012 - 10:56:46
Document(s) archivé(s) le : dimanche 11 novembre 2012 - 02:25:33

### Fichier

Convergence.2012.08.03.pdf
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### Identifiants

• HAL Id : hal-00628086, version 2

### Citation

Julian Tugaut. Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence. 2011. <hal-00628086v2>

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