  The problem of quickest change detection (QCD) under transient dynamics is
studied, where the change from the initial distribution to the final persistent
distribution does not happen instantaneously, but after a series of transient
phases. The observations within the different phases are generated by different
distributions. The objective is to detect the change as quickly as possible,
while controlling the average run length (ARL) to false alarm, when the
durations of the transient phases are completely unknown. Two algorithms are
considered, the dynamic Cumulative Sum (CuSum) algorithm, proposed in earlier
work, and a newly constructed weighted dynamic CuSum algorithm. Both algorithms
admit recursions that facilitate their practical implementation, and they are
adaptive to the unknown transient durations. Specifically, their asymptotic
optimality is established with respect to both Lorden's and Pollak's criteria
as the ARL to false alarm and the durations of the transient phases go to
infinity at any relative rate. Numerical results are provided to demonstrate
the adaptivity of the proposed algorithms, and to validate the theoretical
results.
