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

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

TLDRThe first result that we will use for proving the main theorem describes convergence of the solution to the system.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

3.1 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

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