Sequential Decision Problems for Marked Poisson Processes

This article develops and explores the sequential detection and quickest detection problems for marked Poisson processes. In particular, mixed-differential-difference equations that describe the error probabilities and average sample numbers of the sequential probability ratio test (SPRT), and the average time between false alarms and the average delay until detection of the cumulative sum (CUSUM) test are derived. A numerical technique for solving these equations is described, and this method is used to analyze several examples, revealing some basic properties of these tests.