Optimal speed of detection in generalized Wiener disorder problems.
type: Item
instance of: scholarly article
title: Optimal speed of detection in generalized Wiener disorder problems.
zbMATH Open document ID: 1059.60055
DOI: 10.1016/S0304-4149(01)00098-9
author: J. M. C. Clark
author: M. H. Vellekoop
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: A general Wiener disorder problem is studied where the scalar observation process is defined by \[ dY^\varepsilon _t= S_th(t-\tau )\,dt +\varepsilon \,dW_t, \quad Y_0^\varepsilon =0, \] where \(S_t\) is a right-continuous jump process given as \(S_t=0\) if \(0\leq t<\tau \) and \(S_t= X\) for \(t\geq \tau \), \(X\in \mathbb R \) and \(\tau \in (0,\infty )\) being independent finite random variables with given distribution functions, representing the jump size and the change point, respectively. The aim is to detect a general time profile \(h\) which size \(X\), unlike in the standard Wiener disorder problems, is unknown. The problem is formulated within the Bayesian framework of nonlinear filtering theory. Explicit expressions for the detection delay in the optimal statistics for small noise intensities are given and detection delays of recursive suboptimal detection algorithms are discussed.
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 2138887
zbMATH Keywords: Wiener disorder problem
zbMATH Keywords: detection
zbMATH Keywords: nonlinear filtering
MaRDI profile type: Publication
cites work: Q3121550
cites work: Q3348836
cites work: Q3908216
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cites work: A diffusion process and its applications to detecting a change in the drift of Brownian motion
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full work available at URL: s0304-4149(01)00098-9
OpenAlex ID: W2113386740
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description: scientific article; zbMATH DE number 2138887