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Chronopoulou, Alexandra; Fellouris, Georgios

Optimal sequential change detection for fractional diffusion-type processes. (English) Zbl 1349.62368

J. Appl. Probab. 50, No. 1, 29-41 (2013).
Summary: 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 \(H+1/2\).

Cited in 2 Documents

MSC:

62L10 Sequential statistical analysis
60G22 Fractional processes, including fractional Brownian motion
62L12 Sequential estimation
60G40 Stopping times; optimal stopping problems; gambling theory
60J60 Diffusion processes

Keywords:

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

Software:

longmemo
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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