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Large Deviations for Markov Chains.
・ISBN 978-1-316-51189-3 hard GB£ 104.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-05312-9
| 著者・編者 | de Acosta, Alejandro D., |
|---|---|
| シリーズ | Cambridge Tracts in Mathematics |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2022 |
| ページ数 | 230 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-16041＞ |
解説
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.