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Some first passage problems related to cusum procedures

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  • Khan, Rasul A.

Abstract

Let X1,X2,... be independent random variables, and set Wn = max(0,Wn-1 + Xn), W0 = 0, n [greater-or-equal, slanted] 1. The so-called cusum (cumulative sum) procedure uses the first passage time T(h) = inf{n [greater-or-equal, slanted] 1: Wn[greater-or-equal, slanted]h}for detecting changes in the mean [mu] of the process. It is shown that limh-->[infinity] [mu]ET(h)/h = 1 if [mu] > 0. Also, a cusum procedure for detecting changes in the normal mean is derived when the variance is unknown. An asymptotic approximation to the average run length is given.

Suggested Citation

  • Khan, Rasul A., 1979. "Some first passage problems related to cusum procedures," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 207-215, November.
    • Handle: RePEc:eee:spapps:v:9:y:1979:i:2:p:207-215
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    Cited by:

    1. V. Abramov & M. K. Khan & R. A. Khan, 2008. "A probabilistic analysis of the trading the line strategy," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 499-512.

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