A Sequential Detection Theory for Statistically Periodic Random Processes

Periodic statistical behavior of data is observed in many practical problems encountered in cyber-physical systems and biology. A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to model such data. An optimal stopping theory is developed to solve sequential detection problems for i.p.i.d. processes. The developed theory is then applied to detect a change in the distribution of an i.p.i.d. process. It is shown that the optimal change detection algorithm is a stopping rule based on a periodic sequence of thresholds. Numerical results are provided to demonstrate that a single-threshold policy is not strictly optimal.