Details

Autor(en) / Beteiligte

• Donati-Martin, Catherine
• Lejay, Antoine
• Rouault, Alain

Titel

On the Markovian Similarity

Ist Teil von

• Séminaire de Probabilités XLIX, 2018, Vol.2215, p.375-403

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Two finite Markov generators L and L˜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde L$$ \end{document} are said to be intertwined if there exists a Markov kernel Λ such that LΛ=ΛL˜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$L\varLambda =\varLambda \widetilde L$$ \end{document}. The goal of this paper is to investigate the equivalence relation between finite Markov generators obtained by imposing mutual intertwinings through invertible Markov kernels, in particular its links with the traditional similarity relation. Some consequences on the comparison of speeds of convergence to equilibrium for finite irreducible Markov processes are deduced. The situation of infinite state spaces is also quickly mentioned, by showing that the Laplacians of isospectral compact Riemannian manifolds are weakly Markov-similar.