and the distribution of digital products.
Exit-Problem for a Class of Non-Markov Processes With Path Dependency
1.2 Some remarks on dynamics and initial condition
2.1 Establishing the LDP for the SID
2.2 Results related to the LDP
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
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:::info This paper is available on arxiv under CC BY-SA 4.0 DEED license.
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:::info 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.
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