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This article is cited in 13 scientific papers (total in 13 papers)
On repetitions of long tuples in a Markov chain
V. G. Mikhailova, A. M. Shoitovb a Steklov Mathematical Institute of Russian Academy of Sciences
b Academy of Criptography of Russia
Abstract:
Let $X_0,X_1,\ldots$ be a simple ergodic finite Markov chain. We prove limit theorems for the distribution of the number $\tilde\xi(s,n)$ of events $$\{X_{i-1}\ne X_{j-1},\ X_{i+k}= X_{j+k},\ k=0,\ldots,s-1\},\quad 1\le i<j\le n,$$ when $s,n\to\infty$. Limit theorems for distributions of some random variables connected with $\tilde\xi(s,n)$ are derived as corollaries.
Keywords:
Markov chain, repetitions of tuples, Poisson limit theorem.
Received: 17.02.2014
Citation:
V. G. Mikhailov, A. M. Shoitov, “On repetitions of long tuples in a Markov chain”, Diskr. Mat., 26:3 (2014), 79–89; Discrete Math. Appl., 25:5 (2015), 295–303
Linking options:
https://www.mathnet.ru/eng/dm1292https://doi.org/10.4213/dm1292 https://www.mathnet.ru/eng/dm/v26/i3/p79
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Abstract page: | 609 | Full-text PDF : | 254 | References: | 67 | First page: | 23 |
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