A Quick Explanation of the Large Deviation Principle

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

2 Large Deviation Principle

In this paper, Large Deviations techniques are widely used. Here, by the Large Deviation Principle (LDP) we mean the following asymptotic behaviour of measures.

where I : B → [0, ∞] is a lower-semicontinuous function (this property defines rate function) whose level sets {x : I(x) ≤ α} are compact subsets of B for any 0 ≤ α < ∞ (which means by definition that the rate function is good).

For more information about LDP, see [DZ10]. Note that our definition of LDP by its appearance deviates from the conventional one, but they are equivalent up to multiplication of the “conventional” rate function by 1/2.