For everyk≥1 consider the waiting time until each pattern of lengthk over a fixed alphabet of sizen appears at least once in an infinite sequence of independent, uniformly distributed random letters. Lettingn→∞ we determine the limiting finite dimensional joint distributions of these waiting times after suitable normalization and
provide an estimate for the rate of convergence. It will turn out that these waiting times are getting independent.
Authors:Rafik Aguech, Sana Louhichi, and Sofyen Louhichi
Newman, C. M., Asymptoticindependence and limit theorems for positively and negatively dependent random variables, in: Y. L. Tong, editor, Inequalities in Statistics and Probability , IMS Lecture Notes-Monograph Series 5 (1984), 127-140. MR 86i:60072