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Best choice from the planar Poisson process

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  • Gnedin, A.V.Alexander V.

Abstract

Various best-choice problems related to the planar homogeneous Poisson process in a finite or semi-infinite rectangle are studied. The analysis is largely based on the properties of the one-dimensional box-area process associated with the sequence of records. We prove a series of distributional identities involving exponential and uniform random variables, and give a resolution to the Petruccelli-Porosinski-Samuels paradox on the coincidence of asymptotic values in certain discrete-time optimal stopping problems.

Suggested Citation

  • Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, June.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:2:p:317-354
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    References listed on IDEAS

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    1. Kühne, Robert & Rüschendorf, Ludger, 2000. "Approximation of optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 301-325, December.
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    4. Goldie, Charles M. & Resnick, Sidney I., 1995. "Many multivariate records," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 185-216, October.
    5. Bruss, F. Thomas & Rogers, L. C. G., 1991. "Embedding optimal selection problems in a Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 267-278, August.
    6. Flatau, J. & Irle, A., 1984. "Optimal stopping for extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 16(1), pages 99-111, January.
    7. Porosinski, Zdzislaw, 2002. "On best choice problems having similar solutions," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 321-327, February.
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