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

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


This content originally appeared on HackerNoon and was authored by Class Path

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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This content originally appeared on HackerNoon and was authored by Class Path


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