We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. This method is new and can be very useful in other applications as well, because it allows the use of the powerful optimal stopping theory for diffusions. An auxiliary optimal stopping problem for a jump-diffusion process is solved by transforming it first into a sequence of optimal stopping problems for a pure diffusion by means of a jump operator. In this paper, optimal Bayesian sequential detection rules are developed for such problems when the marked count data is in the form of independent compound Poisson processes, and the continuously changing signals form a multi-dimensional Wiener process. Earlier work on sequential change detection in continuous time does not provide optimal rules for situations in which several marked count data and continuously changing signals are simultaneously observable. The promptness and accuracy of detection rules improve greatly if multiple independent information sources are available. These problems arise, for example, from managing product quality in manufacturing systems and preventing the spread of infectious diseases. The problem is to detect the disorder time as quickly as possible after it happens and minimize the rate of false alarms at the same time. Suppose that local characteristics of several independent compound Poisson and Wiener processes change suddenly and simultaneously at some unobservable disorder time.
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