March 2013 Optimal sequential change detection for fractional diffusion-type processes
Alexandra Chronopoulou, Georgios Fellouris
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J. Appl. Probab. 50(1): 29-41 (March 2013). DOI: 10.1239/jap/1363784422

Abstract

The problem of detecting an abrupt change in the distribution of an arbitrary, sequentially observed, continuous-path stochastic process is considered and the optimality of the CUSUM test is established with respect to a modified version of Lorden's criterion. We apply this result to the case that a random drift emerges in a fractional Brownian motion and we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H+1/2.

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Alexandra Chronopoulou. Georgios Fellouris. "Optimal sequential change detection for fractional diffusion-type processes." J. Appl. Probab. 50 (1) 29 - 41, March 2013. https://doi.org/10.1239/jap/1363784422

Information

Published: March 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1349.62368
MathSciNet: MR3076770
Digital Object Identifier: 10.1239/jap/1363784422

Subjects:
Primary: 60G22 , 60G35
Secondary: 60G40 , 60L10

Keywords: change-point detection , CUSUM , diffusion-type process , fractional Brownian motion , fractional Ornstein–Uhlenbeck , optimality , Sequential change detection

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 1 • March 2013
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