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Sequential change detection revisited. (English) Zbl 1133.62063
Summary: In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better understanding most well-known criteria and also propose new ones. For a specific new criterion that constitutes an extension of G. Lorden’s [Ann. Math. Stat. 42, 1897–1908 (1971; Zbl 0255.62067)] performance measure, we offer the optimum structure for detecting a change in the constant drift of a Brownian motion and a formula for the corresponding optimum performance.

MSC:
62L10 Sequential statistical analysis
62L15 Optimal stopping in statistics
60G40 Stopping times; optimal stopping problems; gambling theory
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