Long time behavior in locally activated random walks
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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Authors
Meunier, N
Mouhot, C
Roux, R
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.
Description
Keywords
local time, random walk, dynamical transition, non-Gaussian probability distribution, blow-up
Journal Title
Communications in Mathematical Sciences
Conference Name
Journal ISSN
1539-6746
1945-0796
1945-0796
Volume Title
17
Publisher
International Press of Boston