Bernoulli

  • Bernoulli
  • Volume 3, Number 4 (1997), 457-478.

Sequential change-point detection in continuous time when the post-change drift is unknown

M. Beibel

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Abstract

Let Wt(0≤t<∞) denote a Brownian motion process which has zero drift during the time interval [0,ν) and drift θ during the time interval [ν,∞), where θ and ν are unknown. The process W is observed sequentially. The general goal is to find a stopping time T of W that 'detects' the unknown time point ν as soon and as reliably as possible on the basis of this information. Here stopping always means deciding that a change in the drift has already occurred. We discuss two particular loss structures in a Bayesian framework. Our first Bayes risk is closely connected to that of the Bayes tests of power one of Lerche. The second Bayes risk generalizes the disruption problem of Shiryayev to the case of unknown θ.

Article information

Source
Bernoulli, Volume 3, Number 4 (1997), 457-478.

Dates
First available in Project Euclid: 6 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175882219

Mathematical Reviews number (MathSciNet)
MR1483699

Zentralblatt MATH identifier
0910.62076

Keywords
Bayes problems Brownian motion change point sequential detection tests of power one

Citation

Beibel, M. Sequential change-point detection in continuous time when the post-change drift is unknown. Bernoulli 3 (1997), no. 4, 457--478. https://projecteuclid.org/euclid.bj/1175882219


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References

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