Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law
Andrew L. Rukhin
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.
Joint Distribution of Pattern Frequencies and Multivariate Polya-Aeppli Law, Theory of Probability and Its Applications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50909
(Accessed May 27, 2023)