Exit-Problem for a Class of Non-Markov Processes With Path Dependency: A Peek at the Exit-Time

Written by classpath | Published 2025/03/06
Tech Story Tags: class-path | non-markov-processes | what-is-a-non-markov-process | exit-time | large-deviation-principle | what-is-the-ldp | the-ldp-explained | the-sid-explained

TLDRFirst, we present the following assumptions on domain G and geometry of the potentials that drive the system inside the domain.via the TL;DR App

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 Exit-time

First, we present the following assumptions on domain G and geometry of the potentials that drive the system inside the domain.

Assumptions A-2.

Now, let us remind the main theorem before proving it. Under the sets of Assumptions A-1 and A-2 the following theorem holds:

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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Published by HackerNoon on 2025/03/06