Optimal speed of detection in generalized Wiener disorder processes

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

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

Fingerprint

Nonlinear filtering
Disorder
White noise
Nonlinear Filtering
Statistics
Functional Law of the Iterated Logarithm
Unknown

Keywords

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

Cite this

Vellekoop, M.H. ; Clark, J.M.C. / Optimal speed of detection in generalized Wiener disorder processes. In: Stochastic processes and their applications. 2001 ; Vol. 95, No. 1. pp. 25-54.
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Optimal speed of detection in generalized Wiener disorder processes. / Vellekoop, M.H.; Clark, J.M.C.

In: Stochastic processes and their applications, Vol. 95, No. 1, 2001, p. 25-54.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Optimal speed of detection in generalized Wiener disorder processes

AU - Vellekoop, M.H.

AU - Clark, J.M.C

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N2 - 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.

AB - 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.

KW - Large deviations

KW - Nonlinear filtering

KW - Wiener disorder problem

KW - Detection problems

U2 - 10.1016/S0304-4149(01)00098-9

DO - 10.1016/S0304-4149(01)00098-9

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