Results Related to the LDP: An Explanation
by Class PathMarch 5th, 2025
Too Long; Didn't Read
The following lemma generalizes the large deviation principle for the case of converging initial conditions.Companies Mentioned
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
2.2 Results related to the LDP
The following lemma generalizes the large deviation principle for the case of converging initial conditions.
and that proves the first inequality. One can prove the second inequality the same way.
As was pointed out before, convergence of measures in Wasserstein distance gives convergence of respective integrals, since ∇F is Lipschitz continuous [Vil09, Theorem 6.9].
As was pointed out before, lower semicontinuity guarantees that infima of a function are achieved over compact sets. We summarise this property by the following corollary.
This paper is available on arxiv under CC BY-SA 4.0 DEED license.
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.
L O A D I N G
. . . comments & more!
. . . comments & more!
