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Markov Chains on Metric Spaces

Af: Tobias Hurth, Michel Benaim Engelsk Paperback
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Markov Chains on Metric Spaces

Af: Tobias Hurth, Michel Benaim Engelsk Paperback
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.
Produktdetaljer
Sprog: Engelsk
Sider: 197
ISBN-13: 9783031118210
Indbinding: Paperback
Udgave:
ISBN-10: 3031118219
Udg. Dato: 22 nov 2022
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Forlag: Springer International Publishing AG
Oplagsdato: 22 nov 2022
Forfatter(e): Tobias Hurth, Michel Benaim
Forfatter(e) Tobias Hurth, Michel Benaim


Kategori Ikke-lineær videnskab


Sprog Engelsk


Indbinding Paperback


Sider 197


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm


Udg. Dato 22 nov 2022


Oplagsdato 22 nov 2022

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