Probability Seminar
Department of Mathematical Sciences |
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Olympia Hadjiliadis Brooklyn College, CUNY
Title: One shot schemes for decentralized quickest change detection.
We consider the problem of sequential detection of a change in the drift of
correlated Brownian motions received in parallel at the sensors of decentralized
systems. We examine the performance of one shot schemes in decentralized detection
in the case of many sensors with respect to appropriate criteria. One shot schemes are schemes in which the sensors
communicate with the fusion center only once; when they must signal a detection. The
communication is clearly asynchronous and we consider the case that the fusion
center employs one of two strategies, the minimal and the maximal. According to the former strategy an alarm is issued at the fusion
center the moment in which the first one of the sensors issues an alarm, whereas
according to the latter strategy an alarm is issued when both sensors have reported
a detection. In this work we derive closed form expressions for the expected delay
of both the minimal and the maximal strategies in the case that CUSUM stopping rules
are employed by the sensors and for specific values of correlation across
sensors. We prove asymptotic optimality of the above strategies in the case of across-sensor independence and specify the optimal threshold selection at the sensors. We also point out the special interpretation of the extreme case of a correlation of -1. Moreover, we discuss extensions of these results in models of more general dependencies in the observations captured by general Ito processes. We set-up appropriate stochastic optimization problems with respect to Kullback-Leibler divergence and discuss optimality issues.
This is joint work with H. Zhang and H.V. Poor
©2008, Department of Mathematical Sciences
Last Modified:
December 4, 2008