Large deviations for additive functionals of Markov chains
- Responsibility
- Alejandro D. de Acosta, Peter Ney.
- Publication
- Providence, Rhode Island : American Mathematical Society, 2014.
- Copyright notice
- ©2013.
- Physical description
- v, 108 pages ; 26 cm.
- Series
- Memoirs of the American Mathematical Society ; no. 1070.
Access
Science Library (Li and Ma)
Serials
| Call number | Status |
|---|---|
| Shelved by Series title NO.1070 |
More options
Creators/Contributors
- Author/Creator
- Acosta, Alejandro D. de, 1941- author.
- Contributor
- Ney, Peter, 1930- author.
Contents/Summary
- Bibliography
- Includes bibliographical references.
- Contents
-
- Introduction The transform kernels Kg and their convergence parameters Comparison of ?(g) and ? ? (g) Proof of Theorem 1 A characteristic equation and the analyticity of ? f : the case when P has an atom C?S satisfying ? (C)>0 Characteristic equations and the analyticity of ? f: the general case when P is geometrically ergodic Differentiation formulas for u g and ? f in the general case and their consequences Proof of Theorem 2 Proof of Theorem 3 Examples Applications to an autoregressive process and to reflected random walk Appendix Background comments References.
- (source: Nielsen Book Data)9780821890899 20160612
- Publisher's Summary
- For a Markov chain {X?} with general state space S and f:S?R ?, the large deviation principle for {n ?1 ? ??=1 f(X?)} is proved under a condition on the chain which is weaker than uniform recurrence but stronger than geometric recurrence and an integrability condition on f , for a broad class of initial distributions. This result is extended to the case when f takes values in a separable Banach space. Assuming only geometric ergodicity and under a non-degeneracy condition, a local large deviation result is proved for bounded f. A central analytical tool is the transform kernel, whose required properties, including new results, are established. The rate function in the large deviation results is expressed in terms of the convergence parameter of the transform kernel.
(source: Nielsen Book Data)9780821890899 20160612
Subjects
Bibliographic information
- Publication date
- 2014
- Copyright date
- 2013
- Series
- Memoirs of the American Mathematical Society ; Number 1070
- Note
- "March 2014, volume 228, number 1070 (second of 5 numbers)."
- ISBN
- 9780821890899 (alk. paper)
- 0821890891 (alk. paper)
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