Distribution of the Number of Successes in Success Runs of Length at Least <Emphasis Type="Italic">k</Emphasis> in Higher-Order Markovian Sequences

We consider the distribution of the number of successes in success runs of length at least k in a binary sequence. One important application of this statistic is in the detection of tandem repeats among DNA sequence segments. In the literature, its distribution has been computed for independent sequences and Markovian sequences of order one. We extend these results to Markovian sequences of a general order. We also show that the statistic can be represented as a function of the number of overlapping success runs of lengths k and k + 1 in the sequence, and give immediate consequences of this representation. AMS 2000 Subject Classification 60E05, 60J05