Langevin process reflected on a partially elastic boundary II

Abstract : A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the critical value 0.1630, the bounces of the reflected process accumulate in a finite time. We show that nonetheless the particle is not necessarily absorbed after this time. We define a "resurrected" reflected process as a recurrent extension of the absorbed process, and study some of its properties. We also prove that this resurrected reflected process is the unique solution to the stochastic partial differential equation describing the model. Our approach consists in defining the process conditioned on never being absorbed, via an h-transform, and then giving the Ito excursion measure of the recurrent extension thanks to a formula fairly similar to Imhof's relation.
Type de document :
Pré-publication, Document de travail
27 pages, 1 figure. This article follows naturally the article "Langevin process reflected on a p.. 2011
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https://hal.archives-ouvertes.fr/hal-00577024
Contributeur : Emmanuel Jacob <>
Soumis le : mercredi 16 mars 2011 - 08:39:47
Dernière modification le : mercredi 12 octobre 2016 - 01:04:39

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  • HAL Id : hal-00577024, version 1
  • ARXIV : 1103.2845

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UPMC | PMA | INSMI | USPC

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Emmanuel Jacob. Langevin process reflected on a partially elastic boundary II. 27 pages, 1 figure. This article follows naturally the article "Langevin process reflected on a p.. 2011. <hal-00577024>

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