Optimal speed of detection in generalized Wiener disorder problems


Vellekoop, M.H. and Clark, J.M.C. (2001) Optimal speed of detection in generalized Wiener disorder problems. Stochastic Processes and Their Applications, 95 (1). pp. 25-54. ISSN 0304-4149

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Abstract:We define a general Wiener disorder problem in which a sudden change in a time profile of unknown size has to be detected in white noise of small intensity. Since both the time of the change and its size are unknown, this problem is considerably harder than standard Wiener disorder problems where the size of the change is assumed to be known a priori. We formulate the problem within the Bayesian framework of nonlinear filtering theory, and use Strassen's functional law of the iterated logarithm to bound stochastic measures which arise in the nonlinear filtering equations. This leads to explicit expressions for the detection delay in the optimal statistics for small noise intensities, and we indicate how these can be used to analyse the detection delays of recursive suboptimal detection algorithms for this problem.
Item Type:Article
Copyright:© 2001 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/74588
Official URL:https://doi.org/10.1016/S0304-4149(01)00098-9
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