Table of Links
Abstract and 1 Introduction
1.1 State of the art
1.2 Some remarks on dynamics and initial condition
1.3 Outline of the paper
1.4 List of notations
2 Large Deviation Principle
2.1 Establishing the LDP for the SID
2.2 Results related to the LDP
2.3 Compactness results
3 Exit-time
3.1 Auxiliary results
3.2 Proof of the main theorem
3.3 Proofs of auxiliary lemmas
4 Generalization and References
Abstract
We are interested in small-noise ( σ → 0) behaviour of exit-time from the potentials’ domain of attraction. In this work rather weak assumptions on potentials V and F, and on domain G are considered. In particular, we do not assume V nor F to be either convex or concave, which covers a wide range of self-attracting and self-avoiding stochastic processes possibly moving in a complex multi-well landscape. The Large Deviation Principle for Self-interacting diffusion with generalized initial conditions is established. The main result of the paper states that, under some assumptions on potentials V and F, and on domain G, Kramers’ type law for the exit-time holds. Finally, we provide a result concerning the exit-location of the diffusion.
1 Introduction
Authors:
(1) Ashot Aleksian, Université Jean Monnet, Institut Camille Jordan, 23, rue du docteur Paul Michelon, CS 82301, 42023 Saint-Étienne Cedex 2, France;
(2) Aline Kurtzmann, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France;
(3) Julian Tugaut, Université Jean Monnet, Institut Camille Jordan, 23, rue du docteur Paul Michelon, CS 82301, 42023 Saint-Étienne Cedex 2, France.
