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Sequential detection of transient changes in stochastic systems under a sampling constraint

The problem of detecting a transient change in distribution of a discrete time series is investigated when there is a constraint on the number of observed samples. Under a minimax setting where the change time is unknown, the objective is to design a statistical test that minimizes a measure of worst case delay under a constraint on the average time to false alarm as well as a constraint on the sampling rate. Leveraging the results in the non-transient setting, it is shown that under full sampling there exists an asymptotic threshold on the minimum duration of a change that can be detected reliably with such false alarm constrained tests. Next, given a transient change with duration above this asymptotic threshold, the smallest sampling rate for which the change can be detected as efficiently as under full sampling is characterized asymptotically.