Ergodicity of Markov processes via nonstandard analysis / Haosui Duanmu, Jeffrey S. Rosenthal, William Weiss.
| Author/creator | Duanmu, Haosui |
| Other author | Rosenthal, Jeffrey S. (Jeffrey Seth) |
| Other author | Weiss, William, 1949- |
| Format | Electronic |
| Publication Info | Providence : American Mathematical Society, [2021] |
| Description | v, 114 pages ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; Volume 273, Number 1342 (fifth of 5 numbers) |
| Abstract | "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. |
| Bibliography note | Includes bibliographical references (pages 113-114). |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2022007656 |
| ISBN | 9781470450021 (paperback) |
| ISBN | (epub) |