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 âV , âF (Assumption A-1.ii) and get:
Therefore, by Grönwallâs inequality
it means the continuity of the map G for any possible x â X.
This paper is available on arxiv under CC BY-SA 4.0 DEED license.
Authors:
(1) Ashot Aleksian, UniversitĂ© Jean Monnet, Institut Camille Jordan, 23, rue du docteur Paul Michelon, CS 82301, 42023 Saint-Ătienne Cedex 2, France;
(2) Aline Kurtzmann, Université de Lorraine, CNRS, Institut Elie Cartan de Lorraine UMR 7502, Vandoeuvre-lÚs-Nancy, F-54506, France;
(3) Julian Tugaut, UniversitĂ© Jean Monnet, Institut Camille Jordan, 23, rue du docteur Paul Michelon, CS 82301, 42023 Saint-Ătienne Cedex 2, France.