Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7550275 | Stochastic Processes and their Applications | 2018 | 33 Pages |
Abstract
Let X1,⦠and Y1,⦠be random sequences taking values in a finite set A. We consider a similarity score LnâL(X1,â¦,Xn;Y1,â¦,Yn) that measures the homology of words (X1,â¦,Xn) and (Y1,â¦,Yn). A typical example is the length of the longest common subsequence. We study the order of moment E|LnâELn|r in the case where the two-dimensional process (X1,Y1),(X2,Y2),⦠is a Markov chain on AÃA. This general model involves independent Markov chains, hidden Markov models, Markov switching models and many more. Our main result establishes a condition that guarantees that E|LnâELn|rânr2. We also perform simulations indicating the validity of the condition.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jüri Lember, Heinrich Matzinger, Joonas Sova, Fabio Zucca,