This paper studies the joint distribution of frequencies of several overlapping words in a Markov sequence. Usually, characteristics of this distribution are expressed in terms of so-called pattern correlation matrix. A more direct approach allows for explicit formulas which involve the fundamental matrix of the Markov chain whose states are patterns of a given length. this form leads to the probability generating function of the asymptotic joint distribution of pattern frequencies.
Citation: Theory of Probability and Its Applications
Pub Type: Journals
Compound Poisson approximation, Fundamental matrix, Markov sequences, Pattern Correlation Matrices, Polya-Aeppli distribution