A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations

Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{1,\dots,d\}^{{\mathbb{N}}}$\end{document} (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext] is a discrete time Ruelle operator (transfer operator), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A:\{1,\dots,d\}^{{\mathbb{N}}}\to\mathbb{R}$\end{document} is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability.