Joint Distribution of Pattern Frequencies and Multivariate Pòlya–Aeppli Law
Andrew L. Rukhin · Theory of Probability and Its Applications · 2010
The paper studies the joint distribution of frequencies of overlapping words in a Markov sequence. Usually characteristics of this distribution are expressed in terms of a 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 words of a given length. These formulas lead to the probability generating function of the asymptotic joint distribution of pattern frequencies corresponding to a new multivariate discrete distribution.