Strong Law of Large Numbers for Hidden Markov Chains Indexed by Cayley Trees

Huang, Huilin

doi:10.5402/2012/768657

ISRN Probability and Statistics

2012

DOI: 10.5402/2012/768657

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Strong Law of Large Numbers for Hidden Markov Chains Indexed by Cayley Trees

Huilin Huang

Abstract: We extend the idea of hidden Markov chains on lines to the situation of hidden Markov chains indexed by Cayley trees. Then, we study the strong law of large numbers for hidden Markov chains indexed by Cayley trees. As a corollary, we get the strong limit law of the conditional sample entropy rate.

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2022

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Asymptotic properties of words in semi-Markov sequences

2022

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It is well known that some enzymes, proteins, amino-acids between other biological molecules have more than one way to be coded in the DNA. That means, there are some biological molecules that can be identified by a set of sequences. For instance, the enzyme SmaI can be recognized by the words [Formula: see text] and [Formula: see text]. In this paper, we count the number of times that a biological sequence occurs through the DNA by any of its configurations, i.e. we provide the strong law of large numbers for a word sequence. To achieve our goal, we consider that DNA is modeled by an ergodic semi-Markov chain. We also present the Central Limit Theorem. Additionally, we compute the first hitting position of a set of words.

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Asymptotic properties of words in semi-Markov sequences

2022

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Strong Law of Large Numbers for Hidden Markov Chains Indexed by Cayley Trees

Cited by 1 publication

References 11 publications

Asymptotic properties of words in semi-Markov sequences

Asymptotic properties of words in semi-Markov sequences

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