The theory of large deviations is concerned with the exponential decay of probabilities of
large fluctuations in random systems. These probabilities are important in many fields of …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic
spin system with a Glauber dynamics in a finite two dimensional torus under a positive …

We consider the exit event from a metastable state for the overdamped Langevin dynamics
dX_t=-∇ f (X_t) dt+ h dB_t d X t=-∇ f (X t) dt+ hd B t. Using tools from semiclassical analysis …

We consider a class of Glauber dynamics for the two-dimensional nearest neighbor
ferromagnetic Ising model in which the rate with which each spin flips depends only on the …

There is a long history in ecology of using mathematical models to identify deterministic
processes that may lead to dramatic population dynamic patterns like boom-and-bust …

We apply previous results on the pathwise exponential loss of memory of the initial condition
for stochastic differential equations with small diffusion to the problem of the asymptotic …

Summary We study the Zero White Noise Limit for diffusions in a continuous
multidimensional medium: given a continuous function on ℝ n, W, we consider diffusions …

For ϵ> 0, we consider the valued Markov process whose generator is. X ϵ is a small random
perturbation of the deterministic dynamical system. We first establish rough asymptotics for …

We consider a dynamical system in driven by a vector field-U', where U is a multi-well
potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy …