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Sequential testing of simple hypotheses about compound Poisson processes

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  • Dayanik, Savas
  • Sezer, Semih O.

Abstract

One of two simple hypotheses for the unknown arrival rate and jump distribution of a compound Poisson process is correct. We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision. We find a Bayes-optimal sequential decision rule and describe completely how to calculate its parameters without any restrictions on the arrival rate and the jump distribution.

Suggested Citation

  • Dayanik, Savas & Sezer, Semih O., 2006. "Sequential testing of simple hypotheses about compound Poisson processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1892-1919, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1892-1919
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    References listed on IDEAS

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    1. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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    Cited by:

    1. Ali Devin Sezer & Çağrı Haksöz, 2012. "Optimal Decision Rules for Product Recalls," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 399-418, August.
    2. Savas Dayanik & Semih Sezer, 2012. "Multisource Bayesian sequential binary hypothesis testing problem," Annals of Operations Research, Springer, vol. 201(1), pages 99-130, December.
    3. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.

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