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Some results associated with the longest run in a strongly ergodic Markov chain.
- Source :
-
Acta Mathematica Sinica . Oct2013, Vol. 29 Issue 10, p1939-1948. 10p. - Publication Year :
- 2013
-
Abstract
- This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain. Let $$\left\{ {X_a } \right\}_{a \in Z_ + }$$ be a stationary strongly ergodic reversible Markov chain on countablestate space S = {1, 2, ...}. Let T ā S be an arbitrary finite subset of S. Denote by Ln the length of the longest run of consecutive iās for i ā T, that occurs in the sequence X1, ..., Xn. In this paper, we obtain a limit law and a week version of an Erdös-Rényi type law for Ln. A large deviation result of Ln is also discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 29
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 90133111
- Full Text :
- https://doi.org/10.1007/s10114-013-2549-6