Optimal sequential change detection for fractional diffusion-type processes

Research output: Contribution to journalArticlepeer-review

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 .

Original languageEnglish (US)
Pages (from-to)29-41
Number of pages13
JournalJournal of Applied Probability
Volume50
Issue number1
DOIs
StatePublished - Mar 2013
Externally publishedYes

Keywords

  • CUSUM
  • Change-point detection
  • Diffusion-type process
  • Fractional brownian motion
  • Fractional ornstein-uhlenbeck
  • Optimality
  • Sequential change detection

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty

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