Optimal sequential change-detection for fractional stochastic differential equations

Details Optimal sequential change-detection for fractional stochastic differential equations Optimal sequential change-detection for fractional stochastic differential equations

2011-02-03

arxiv.org/abs/1102.0598v1

Mathematics

Statistics Theory

23 pages, 3 figures

Scientific paper

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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