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

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


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 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:

\

\

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

:::

:::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.

:::

\


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


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