Ergodicity of Markov Processes via Nonstandard Analysis (Memoirs of the American Mathematical Society) - Softcover

Haosui Duanmu (author); Jeffrey S. Rosenthal (author) & William Weiss (author)

Softcover

ISBN 10: 147045002X ISBN 13: 9781470450021

Publisher: American Mathematical Society, 2022

Synopsis

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.

About this title

About the Author

Haosui Duanmu, University of Toronto, ON, Canada.

Jeffrey S. Rosenthal, University of Toronto, ON, Canada.

William Weiss, University of Toronto, ON, Canada.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 147045002X
• ISBN 13: 9781470450021
• Binding: Paperback
• Number of pages: 277