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Optimal Sequential Change Detection for Fractional Diffusion-Type Processes

Part of: Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Alexandra Chronopoulou  and
Georgios Fellouris
Alexandra Chronopoulou*
Affiliation:
University of California, Santa Barbara
Georgios Fellouris*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA. Email address: chronopoulou@pstat.ucsb.edu
∗∗ Postal address: Department of Mathematics, 3620 South Vermont Avenue, Los Angeles, CA 90089, USA. Email address: fellouri@usc.edu
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Abstract

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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.

Keywords

CUSUMsequential change detectionchange-point detectionfractional Brownian motionfractional Ornstein–Uhlenbeckdiffusion-type processoptimality

MSC classification

Primary: 60G35: Signal detection and filtering 60G22: Fractional processes, including fractional Brownian motion
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 29 - 41
Copyright
Copyright © Applied Probability Trust 2013 

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