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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Markov Chains on Metric Spaces: A Short Course

Markov Chains on Metric Spaces: A Short Course

Benaïm, Michel
Hurth, Tobias

Paperback

Series: Universitext

Technology & EngineeringGeneral MathematicsProbability & Statistics

ISBN10: 3031118219
ISBN13: 9783031118210
Publisher: Springer Nature
Published: Nov 22 2022
Pages: 197
Weight: 0.68
Height: 0.46 Width: 6.14 Depth: 9.21
Language: English
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.

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