Journal of Applied Probability
- J. Appl. Probab.
- Volume 50, Number 1 (2013), 29-41.
Optimal sequential change detection for fractional diffusion-type processes
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.
J. Appl. Probab., Volume 50, Number 1 (2013), 29-41.
First available in Project Euclid: 20 March 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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