Stochastic renewal equation for the waiting time statistics for the first occurrence of a specific sequence of states successively visited by an alternating renewal process
Abstract:
Both Markovian and arbitrary residence time distributions are considered. The comparison of analytical predictions with the case of a time-decorrelated process shows that correlations can both decrease and increase the corresponding expected waiting time. Besides, the comparison of exponential, subexponential, and heavy-tailed models characterized by equal probabilities to observe the event of interest demonstrates that a faster decrease in the residence time probability density implies a shorter expected waiting time. Interestingly, irrespective of the details of a particular model for both discrete- and continuous-time jump processes considered here, the random waiting time becomes exponentially distributed in the long-time limit, thus, showing remarkable universality.
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