Ergodicity of Markov processes via nonstandard analysis / Haosui Duanmu, Jeffrey S. Rosenthal, William Weiss.

Author
Duanmu, Haosui [Browse]
Format
Book
Language
English
Published/​Created
Providence : American Mathematical Society, [2022]
Description
v, 114 pages ; $$c 26 cm

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Lewis Library - Stacks QA3 .A57 no.1342 Browse related items Request

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    Summary note
    "The Markov chain ergodic theorem is well-understood if either the time-line or the state space is discrete. However, there does not exist a very clear result for general state space continuous-time Markov processes. Using methods from mathematical logic and nonstandard analysis, we introduce a class of hyperfinite Markov processes-namely, general Markov processes which behave like finite state space discrete-time Markov processes. We show that, under moderate conditions, the transition probability of hyperfinite Markov processes align with the transition probability of standard Markov processes. The Markov chain ergodic theorem for hyperfinite Markov processes will then imply the Markov chain ergodic theorem for general state space continuous-time Markov processes"-- Provided by publisher.
    Bibliographic references
    Includes bibliographical references.
    ISBN
    • 9781470450021 ((paperback))
    • 147045002X
    LCCN
    2022007656
    OCLC
    1313792933
    Statement on language in description
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