Sooner and later waiting time problems for Markovian Bernoulli trials (Q689497)

The waiting time problems discussed by \textit{M. Ebneshahrashoob} and \textit{M. Sobel} [ibid. 9, No. 1, 5-11 (1990; Zbl 0695.60016)] are generalized to the case when the Bernoulli trials are correlated in a Markovian fashion. The waiting times arise by setting quotas on both runs and frequencies of successes and failures. The `sooner cases' refer to situations in which experimentation stops as soon as one of the quotas is reached, while the `later cases' bring the experiment to a halt when both quotas are completed. The results can also be extended to higher-order dependence models. To illustrate the methods of analysis, a simple model for individual learning is briefly discussed.