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On repetitions of long tuples in a Markov chain
-
Vladimir G. Mikhaylov
und
Aleksandr M. Shoytov
Veröffentlicht/Copyright:
8. Dezember 2015
Abstract
Let X0,X1, . . . be a simple ergodic finite Markov chain.We prove limit theorems for the distribution of the number ξ̄(s, n) of events
{Xi−1 ≠ Xj−1, Xi+k = Xj+k, k = 0, . . . , s − 1}, 1 ≤ i < j ≤ n,
when s, n → ∞. Limit theorems for distributions of some random variables connected with ξ̄(s, n) are derived as corollaries.
Received: 2014-2-17
Published Online: 2015-12-8
Published in Print: 2015-10-1
© 2015 by Walter de Gruyter Berlin/Boston
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Artikel in diesem Heft
- Frontmatter
- On groups of even orders with automorphisms generating recurrent sequences of the maximal period
- Local contractivity of the process of a player rating variation in the Elo model with one adversary
- On regular hypergraphs with high girth and high chromatic number
- On repetitions of long tuples in a Markov chain
- Automorphism-extendable modules
- On read-once transformations of random variables over finite fields
Artikel in diesem Heft
- Frontmatter
- On groups of even orders with automorphisms generating recurrent sequences of the maximal period
- Local contractivity of the process of a player rating variation in the Elo model with one adversary
- On regular hypergraphs with high girth and high chromatic number
- On repetitions of long tuples in a Markov chain
- Automorphism-extendable modules
- On read-once transformations of random variables over finite fields
