Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: October 25, 2001
Language: eng
Format: Paperback
Number of pages: 145
ISBN-13: 9783540424154
Subjects: Calculus & mathematical analysis; Stochastics; Probabilities; Limit theorems (Probability th; Science/Mathematics; Mathematics; Medical / Nursing; Limit theorems (Probability theory); Differential Equations; General; Probability & Statistics - General; Limit theorems; Markov chain; Mathematics / Statistics; Mathematics-Differential Equations; Mathematics-Probability & Statistics - General; Medical / General; Stochastic processes; Differentiable Dynamical Systems; Differentiable dynamical syste; Markov processes
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.