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On the rate of convergence for the length of the longest common subsequences in hidden Markov models

Part of: Limit theorems Combinatorial probability Combinatorics

Published online by Cambridge University Press:  30 July 2019

C. Houdré  and
G. Kerchev
C. Houdré*
Affiliation:
Georgia Institute of Technology
G. Kerchev*
Affiliation:
Georgia Institute of Technology
*
*Postal address: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street Atlanta, GA 30332-0160, USA.
*Postal address: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street Atlanta, GA 30332-0160, USA.
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Abstract

Let (X, Y) = (Xn, Yn)n≥1 be the output process generated by a hidden chain Z = (Zn)n≥1, where Z is a finite-state, aperiodic, time homogeneous, and irreducible Markov chain. Let LCn be the length of the longest common subsequences of X1,..., Xn and Y1,..., Yn. Under a mixing hypothesis, a rate of convergence result is obtained for E[LCn]/n.

Keywords

Longest common subsequencerate of convergencehidden Markov modelHoeffding inequalitymixing condition

MSC classification

Primary: 60C05: Combinatorial probability 05A05: Permutations, words, matrices
Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 558 - 573
Copyright
© Applied Probability Trust 2019 

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