Exit-Problem for a Class of Non-Markov Processes With Path Dependency: A List of Notations

by Class PathMarch 5th, 2025
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The paper contains number of technical results. To make them more reader-friendly, we present here a list of notions

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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

1.4 List of notations

The paper contains number of technical results. To make them more reader-friendly, we present here a list of notions that are used later in the paper.



All the equations in the paper are meant to hold a.s. unless stated otherwise.


This paper is available on arxiv under CC BY-SA 4.0 DEED license.

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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