Title: Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness
Description: This book shows how techniques from the perturbation theory of operators, applied to a quasi-compact positive kernel, may be used to obtain limit theorems for Markov chains or to describe stochastic properties of dynamical systems. A general framework for this method is given and then applied to treat several specific cases. An essential element of this work is the description of the peripheral spectra of a quasi-compact Markov kernel and of its Fourier-Laplace perturbations. This is first done in the ergodic but non-mixing case. This work is extended by the second author to the non-ergodic case. The only prerequisites for this book are a knowledge of the basic techniques of probability theory and of notions of elementary functional analysis.
Subjects: Stochastic processes, Limit theorems (Probability theory), Differentiable dynamical systems, Markov processes, Dynamische systemen, Markov-Kette, Théorèmes limites (Théorie des probabilités), Dynamisches System, Processus de Markov, Markov-processen, Stochastische parameters, Dynamique différentiable, Grenzwertsatz, Processus stochastiques, Stochastischer Prozess, Mathematics, Differential Equations, Distribution (Probability theory)