A martingale minimax exponential inequality for Markov chains - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

A martingale minimax exponential inequality for Markov chains

Résumé

We prove a new inequality controlling the large deviations of the empirical measure of a Markov chain. This inequality is based on the martingale used by Donsker and Varadhan and the minimax theorem. It holds for convex sets and it requires to take an infimum over the starting point. In the case of a compact space, this inequality is a partial improvement of the large deviations estimates of Donsker and Varadhan. In the case of a non compact space, we condition on the event that the process visits n times a compact subset of the space and we still obtain a control on the exponential scale.
Fichier principal
Vignette du fichier
MC.pdf (270.29 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03845287 , version 1 (09-11-2022)

Identifiants

  • HAL Id : hal-03845287 , version 1

Citer

Raphaël Cerf. A martingale minimax exponential inequality for Markov chains. 2022. ⟨hal-03845287⟩
3 Consultations
8 Téléchargements

Partager

Gmail Facebook X LinkedIn More