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Abstract  

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.

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Newman, C. M., Asymptotic independence 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

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Ann. Statist. 1983 11 286 295 Newman, C. M. , Asymptotic independence and

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