Book Details
Format
Paperback / Softback
Book Series
Universitext
ISBN-10
3031118219
ISBN-13
9783031118210
Edition
1st ed. 2022
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Nov 22nd, 2022
Print length
197 Pages
Product Classification:
Cybernetics & systems theoryProbability & statisticsStochastics
Ksh 6,650.00
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This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. The book can serve as the core for a semester- or year-long graduate course in probability theory withan emphasis on Markov chains or random dynamics.
This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space.
The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes.
The book can serve as the core for a semester- or year-long graduate course in probability theory with an emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.
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