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A note on optimal stopping for possible change in the intensity of an ordinary Poisson process

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  • Brown, Marlo
  • Zacks, Shelemyahu

Abstract

Peskir and Shiryaev [2002. Solving the Poisson disorder problem. In: Advances in Finance and Stochastics: Essays in Honor of Dieter Sonderman. Springer, New York, pp. 295-312] determined the optimal stopping rule for a problem of quick detection of a change-point in the intensity of a homogeneous ordinary Poisson process, when the cost per unit time of delayed detection is in a given range, and the change-point occurs at random times following a mixed exponential distribution. Using the same Bayesian framework, we extend their results to a range of cost values not considered before. We obtain the results by using the Dynamic Programming rather than the analytical methods used by Peskir and Shiryaev.

Suggested Citation

  • Brown, Marlo & Zacks, Shelemyahu, 2006. "A note on optimal stopping for possible change in the intensity of an ordinary Poisson process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1417-1425, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:13:p:1417-1425
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    References listed on IDEAS

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    1. Tina Herberts & Uwe Jensen, 2004. "Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 347-366, September.
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    Cited by:

    1. Brown, Marlo, 2008. "Monitoring a Poisson process in several categories subject to changes in the arrival rates," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2637-2643, November.

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    1. Brown, Marlo, 2008. "Monitoring a Poisson process in several categories subject to changes in the arrival rates," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2637-2643, November.

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