Article Dans Une Revue Communications in Mathematical Sciences Année : 2019

Long time behavior in locally activated random walks

Résumé

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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hal-01402104 , version 1 (24-11-2016)

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Nicolas Meunier, Clément Mouhot, Raphaël Roux. Long time behavior in locally activated random walks. Communications in Mathematical Sciences, 2019, 17 (4), pp.1071 - 1094. ⟨10.4310/CMS.2019.v17.n4.a11⟩. ⟨hal-01402104⟩
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