Optimal speed of detection in generalized Wiener disorder problems.
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.
scientific article; zbMATH DE number 2138887
scientific article