This content originally appeared on HackerNoon and was authored by Class Path
Table of Links
1.2 Some remarks on dynamics and initial condition
2.1 Establishing the LDP for the SID
2.2 Results related to the LDP
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.
\
:::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
Class Path | Sciencx (2025-03-05T02:54:26+00:00) A Quick Explanation of the Large Deviation Principle. Retrieved from https://www.scien.cx/2025/03/05/a-quick-explanation-of-the-large-deviation-principle/
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