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We consider the minimax quickest detection problem of an unobservable time of change in the rate of an inhomogeneous Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. In the Wiener case, such a problem has been solved using the so-called cumulative sums (cusum) strategy by Shiryaev [33, 35] , or Moustakides  among others. In ourdoi:10.1214/16-aap1266 fatcat:gij4d6ibivbffl33lpsktjxh3e