On the number of appearances of a word in a sequence of i. i. d. trials
Let \(X_1,\dots,X_n\) be a sequence of independent and identically distributed random variables taking values in a finite alphabet \({\mathcal A}\), whose common distribution is not necessarily uniform. For a given word \(W\) composed of letters of \({\mathcal A}\), bounds are given for the accuracy in total variation of a Poisson approximation to the number \(R(W)\) of appearances of \(W\) as a renewal, and for a compound Poisson approximation to the total number \(N(W)\) of appearances of \(W\). The main tool in the proof is the Stein-Chen method. A number of numerical examples are computed.
scientific article; zbMATH DE number 1394696