3 papers
math.PR2015
A general framework for stochastic traveling waves and patterns, with application to neural field equations
James Inglis, James MacLaurin
In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framewor…
math.PR2014
Asymptotic description of stochastic neural networks. II - Characterization of the limit law
Olivier Faugeras, James MacLaurin
We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H…
math.PR2014
Asymptotic description of stochastic neural networks. I - existence of a Large Deviation Principle
Olivier Faugeras, James MacLaurin
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differe…