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Markov Chains on Metric Spaces

- A Short Course
Af: Michel Benaim, Tobias Hurth Engelsk Paperback

Markov Chains on Metric Spaces

- A Short Course
Af: Michel Benaim, Tobias Hurth Engelsk Paperback
Tjek vores konkurrenters priser
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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 197
ISBN-13: 9783031118210
Indbinding: Paperback
Udgave:
ISBN-10: 3031118219
Kategori: Kybernetik og systemteori
Udg. Dato: 22 nov 2022
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer International Publishing AG
Oplagsdato: 22 nov 2022
Forfatter(e): Michel Benaim, Tobias Hurth
Forfatter(e) Michel Benaim, Tobias Hurth

Kategori Kybernetik og systemteori

ISBN-13 9783031118210

Sprog Engelsk

Indbinding Paperback

Sider 197

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 22 nov 2022

Oplagsdato 22 nov 2022

Forlag Springer International Publishing AG