Journal of Applied Probability

Optimal sequential change detection for fractional diffusion-type processes

Alexandra Chronopoulou and Georgios Fellouris

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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.

Article information

Source
J. Appl. Probab., Volume 50, Number 1 (2013), 29-41.

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1363784422

Digital Object Identifier
doi:10.1239/jap/1363784422

Mathematical Reviews number (MathSciNet)
MR3076770

Zentralblatt MATH identifier
1349.62368

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60G22: Fractional processes, including fractional Brownian motion
Secondary: 60L10 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

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

Citation

Chronopoulou, Alexandra; Fellouris, Georgios. Optimal sequential change detection for fractional diffusion-type processes. J. Appl. Probab. 50 (2013), no. 1, 29--41. doi:10.1239/jap/1363784422. https://projecteuclid.org/euclid.jap/1363784422


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