Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

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

Julian Tugaut

Résumé

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.
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Dates et versions

hal-00628086 , version 1 (30-09-2011)
hal-00628086 , version 2 (10-08-2012)

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  • HAL Id : hal-00628086 , version 2

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

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