Optimal Sequential Change-detection for Fractional Stochastic Differential Equations
نویسندگان
چکیده
The sequential detection of an abrupt and persistent change in the dynamics of an arbitrary continuous-path stochastic process is considered; the optimality of the cumulative sums (cusum) test is established with respect to a modified Lorden’s criterion. As a corollary, sufficient conditions are obtained for the optimality of the cusum test when the observed process is described by a fractional stochastic differential equation. Moreover, a novel family of model-free, Lorden-like criteria is introduced and it is shown that these criteria are optimized by the cusum test when a fractional Brownian motion adopts a polynomial drift. Finally, a modification of the continuous-time cusum test is proposed for the case that only discrete-time observations are available.
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