Mar 04, 2025
Establishing the LDP for the SID: What Does It Mean?
by Class PathMarch 5th, 2025
Too Long; Didn't Read
In this section, we prove LDP for Self-Interacting diffusions of the type (1.7). First, we introduce the following group of main assumptions.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
2.1 Establishing the LDP for the SID
In this section, we prove LDP for Self-Interacting diffusions of the type (1.7). First, we introduce the following group of main assumptions.
Assumptions A-1.
Consider the following theorem that is the main result of the section.
Use Lipschitz continuity of ∇V , ∇F (Assumption A-1.ii) and get:
Therefore, by Grönwall’s inequality
it means the continuity of the map G for any possible x ∈ X.
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.
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