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The problem of quickest change detection (QCD) under transient dynamics isstudied, where the change from the initial distribution to the final persistentdistribution does not happen instantaneously, but after a series of transientphases. The observations within the different phases are generated by differentdistributions. The objective is to detect the change as quickly as possible,while controlling the average run length (ARL) to false alarm, when thedurations of the transient phases are completely unknown. Two algorithms areconsidered, the dynamic Cumulative Sum (CuSum) algorithm, proposed in earlierwork, and a newly constructed weighted dynamic CuSum algorithm. Both algorithmsadmit recursions that facilitate their practical implementation, and they areadaptive to the unknown transient durations. Specifically, their asymptoticoptimality is established with respect to both Lorden's and Pollak's criteriaas the ARL to false alarm and the durations of the transient phases go toinfinity at any relative rate. Numerical results are provided to demonstratethe adaptivity of the proposed algorithms, and to validate the theoreticalresults.

Quickest Change Detection under Transient Dynamics: Theory and Asymptotic Analysis