Excited Brownian Motions
Olivier Raimond (MODAL'X), Bruno Schapira (LM-Orsay)
TL;DR
This paper investigates a continuous-time model of excited random walks, providing key conditions for recurrence and positive speed, extending the understanding of these stochastic processes.
Contribution
It introduces a continuous-time version of excited random walks and establishes necessary and sufficient conditions for recurrence and positive speed.
Findings
Derived a criterion for recurrence.
Established conditions for positive speed.
Extended excited random walk theory to continuous time.
Abstract
We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence and for positive speed. This is analogous to results for excited (or cookie) random walks.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Diffusion and Search Dynamics · Stochastic processes and statistical mechanics