Optimal speed of detection in generalized Wiener disorder processes

M.H. Vellekoop, J.M.C Clark

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)
    21 Downloads (Pure)

    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.
    Original languageEnglish
    Pages (from-to)25-54
    Number of pages29
    JournalStochastic processes and their applications
    Volume95
    Issue number1
    DOIs
    Publication statusPublished - 2001

    Keywords

    • Large deviations
    • Nonlinear filtering
    • Wiener disorder problem
    • Detection problems

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