Convergence theorems for the lengths of consecutive successes of Markov Bernoulli sequences
Y. H. Wang, Hsiao-Fen Chang, Shun‐Yi Chen · Journal of Applied Probability · 2003
The limiting distributions of the sums of the lengths of four different kinds of runs of consecutive successes of Markov Bernoulli sequences are derived. It is shown that the limits are convolutions of several distributions involving the Bernoulli, the geometric and the Poisson or compound Poisson distributions.