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Optimal Sequential Change Detection for Fractional Diffusion-Type Processes

  • Alexandra Chronopoulou (a1) and Georgios Fellouris (a2)

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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Copyright

Corresponding author

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

References

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Keywords

MSC classification

Optimal Sequential Change Detection for Fractional Diffusion-Type Processes

  • Alexandra Chronopoulou (a1) and Georgios Fellouris (a2)

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