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Abstract: The multiple disorder problem seeks to determine a sequence of stopping timeswhich are as close as possible to the unknown times of disorders at which theobservation process changes its probability characteristics. We derive closedform solutions in two formulations of the multiple disorder problem for anobservable Brownian motion with switching constant drift rates. The method ofproof is based on the reduction of the initial problems to appropriate optimalswitching problems and the analysis of the associated coupled free-boundaryproblems. We also describe the sequential switching multiple disorder detectionprocedures resulting from these formulations.



Author: Pavel V. Gapeev

Source: https://arxiv.org/



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