Statistical analysis of the number of self-overlapping leftmost repeats in an homogeneous stationary Markov chain on finite states

ABSTRACT

This article addresses the problem of repeats detection used in the comparison of significant repeats in sequences. The case of self-overlapping leftmost repeats for large sequences generated by an homogeneous stationary Markov chain has not been treated in the literature. In this work, we are interested by the approximation of the number of self-overlapping leftmost long enough repeats distribution in an homogeneous stationary Markov chain. Using the Chen–Stein method, we show that the number of self-overlapping leftmost long enough repeats distribution is approximated by the Poisson distribution. Moreover, we show that this approximation can be extended to the case where the sequences are generated by a m-order Markov chain.