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

Abstract

Let $(X,Y)=(X_n,Y_n{)}_{n\ge 1}$ be the output process generated by a hidden chain $Z=(Z_n{)}_{n\ge 1}$, where $Z$ is a finite state, aperiodic, time homogeneous, and irreducible Markov chain. Let $L{C}_n$ be the length of the longest common subsequences of $X_1,\dots ,X_n$ and $Y_1,\dots ,Y_n$. Under a mixing hypothesis, a rate of convergence result is obtained for $\mathbb{E}[L{C}_n]/n$.

arXiv commentTo appear in Journal of Applied Probability 56.2 (June 2019)