A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials

Abstract

A sequence of independent experiments is performed, each one producing a letter from a given alphabet. We study the number of overlapping appearances of a given pattern of letters and we prove that, under quite general conditions, the number of overlapping appearances of long patterns is approximately distributed according to a Pólya-Aeppli distribution. © 1988 Springer-Verlag.