Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness (Lecture Notes in Mathematics)

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)