TitoloLower bounds for moments of global scores of pairwise Markov chains
Autore/iLember, J.; Matzinger, H., Sova, J.; Zucca, F.
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AbstractLet us consider two random sequences such that every random variable takes values in a finite set. We consider a global similarity score that measures the homology (relatedness) of words obtained by the random sequences. A typical example of such score is the length of the longest common subsequence. We study the order of central absolute r-moment of the score in the case where the two-dimensional joint process represented by the two random sequences is a Markov chain. This is a very general model involving independent Markov chains, hidden Markov models, Markov switching models and many more. Our main result establishes a general condition which allows to obtain an explicit asymptotic value of the central absolute r-moment of the score. We also perform simulations indicating the validity of the condition.