Dynamics and Initial Condition: A Quick Rundown

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

Let us introduce some notation and notions that will be useful to describe laconically later derivations in this paper.

\

\ As before, we define marginal deterministic system that corresponds to the equation (1.7) as

\

\ Hereafter, we will drop one part of the subscript or both (initial conditions and σ) if it is clear which one of the equations is meant. Though, to avoid confusion we will always use the subscript 0 to emphasize that we consider specifically the deterministic system. For x such that Tx = ∞ we naturally extend the definition of the processes (1.7) and (1.8) as

\

\

:::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.

:::

\