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OverviewThe 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. Full Product DetailsAuthor: Haosui Duanmu , Jeffrey S. Rosenthal , William WeissPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.231kg ISBN: 9781470450021ISBN 10: 147045002 Publication Date: 28 February 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationHaosui Duanmu, University of Toronto, ON, Canada. Jeffrey S. Rosenthal, University of Toronto, ON, Canada. William Weiss, University of Toronto, ON, Canada. Tab Content 6Author Website:Countries AvailableAll regions |
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