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Long time behavior in locally activated random walks

Abstract : We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient: emergence of a non-Gaussian mul-tipeaked probability distribution and a dynamical transition to an absorbing static state. We compute the generator and we study the partial differential equation which involves its adjoint. We discuss global existence and blow-up of the solution to this latter equation.
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https://hal.archives-ouvertes.fr/hal-01402104
Contributor : Nicolas Meunier <>
Submitted on : Thursday, November 24, 2016 - 11:30:23 AM
Last modification on : Friday, April 10, 2020 - 5:12:37 PM
Document(s) archivé(s) le : Tuesday, March 21, 2017 - 2:28:53 AM

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  • HAL Id : hal-01402104, version 1
  • ARXIV : 1611.08173

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Nicolas Meunier, Clément Mouhot, Raphaël Roux. Long time behavior in locally activated random walks. 2016. ⟨hal-01402104⟩

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