Optimal bounds for bit-sizes of stationary distributions in finite Markov chains - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Optimal bounds for bit-sizes of stationary distributions in finite Markov chains

Mateusz Skomra

Résumé

An irreducible stochastic matrix with rational entries has a stationary distribution given by a vector of rational numbers. We give an upper bound on the lowest common denominator of the entries of this vector. Bounds of this kind are used to study the complexity of algorithms for solving stochastic mean payoff games. They are usually derived using the Hadamard inequality, but this leads to suboptimal results. We replace the Hadamard inequality with the Markov chain tree formula in order to obtain optimal bounds. We also adapt our approach to obtain bounds on the absorption probabilities of finite Markov chains and on the gains and bias vectors of Markov chains with rewards.
Fichier principal
Vignette du fichier
main.pdf (364.24 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03765666 , version 1 (31-08-2022)

Identifiants

Citer

Mateusz Skomra. Optimal bounds for bit-sizes of stationary distributions in finite Markov chains. 2022. ⟨hal-03765666⟩
5 Consultations
13 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More