Exit-Problem for a Class of Non-Markov Processes With Path Dependency: The Auxiliary Results

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

3.1 Auxiliary results 3.1.1 Initial descent to the point of attraction

3.1.2 Convergence of deterministic process towards a

3.1.3 Attraction of stochastic process towards a

3.1.4 Behaviour in the annulus between Bρ(a) and ∂G

3.1.5 Stabilization of the occupation measure

3.1.6 Exit before nearing a

3.1.7 Control of dynamics for small time intervals

3.1.8 Uniform lower bound for probability of exit from G

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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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