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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
Availability
Available Online
Memoirs of the American Mathematical Society (2013-present)
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Status
Location Service
Notes
Lewis Library - Stacks
QA3 .A57 no.1342
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Details
Subject(s)
Markov processes
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Ergodic theory
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Nonstandard mathematical analysis
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Author
Rosenthal, Jeffrey S. (Jeffrey Seth)
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Weiss, William, 1949-
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Series
Memoirs of the American Mathematical Society ; no. 1342.
[More in this series]
Memoirs of the American Mathematical Society, 0065-9266 ; Volume 273, Number 1342 (fifth of 5 numbers)
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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
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Ergodicity of Markov processes via nonstandard analysis / Haosui Duanmu, Jeffrey S. Rosenthal, William Weiss.
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99125518423706421