IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v111y2004i2p317-354.html
   My bibliography  Save this article

Best choice from the planar Poisson process

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00002-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kühne, Robert & Rüschendorf, Ludger, 2000. "Approximation of optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 301-325, December.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. Flatau, J. & Irle, A., 1984. "Optimal stopping for extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 16(1), pages 99-111, January.
    6. Porosinski, Zdzislaw, 2002. "On best choice problems having similar solutions," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 321-327, February.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    8. Bruss, F. Thomas & Paindaveine, Davy, 2000. "Selecting a sequence of last successes in independent trials," MPRA Paper 21166, University Library of Munich, Germany.
    9. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    10. Porosinski, Zdzislaw, 1987. "The full-information best choice problem with a random number of observations," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 293-307, May.
    11. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    12. Bojdecki, Tomasz, 1978. "On optimal stopping of a sequence of independent random variables -- probability maximizing approach," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 153-163, January.
    13. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    14. Goldie, Charles M. & Resnick, Sidney I., 1995. "Many multivariate records," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 185-216, October.
    15. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jeongmi Jeong & Chan-Gyun Kim, 2020. "Existence of Positive Solutions to Singular φ -Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    2. C.V.O. Eneji & E. Obim & J.E.O. Eneji & T.O. Ellah & A. Ushie, 2013. "Civil Societies/Non- Governmental Organizations as Catalysts for the Attainment of the Millennium Development Goals in Nigeria," International Journal of Management Sciences, Research Academy of Social Sciences, vol. 1(11), pages 427-435.
    3. Ehsan Pourhadi & Reza Saadati & Sotiris K. Ntouyas, 2019. "Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    4. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    5. Christopher S. Goodrich, 2021. "A topological approach to nonlocal elliptic partial differential equations on an annulus," Mathematische Nachrichten, Wiley Blackwell, vol. 294(2), pages 286-309, February.
    6. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    7. Youwei Zhang, 2014. "Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces," International Journal of Analysis, Hindawi, vol. 2014, pages 1-18, May.
    8. Maloni, Michael & Jackson, Eric C., 2005. "North American Container Port Capacity," 46th Annual Transportation Research Forum, Washington, D.C., March 6-8, 2005 208147, Transportation Research Forum.
    9. T. Jankowski & R. Jankowski, 2010. "Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 105-115, July.
    10. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    11. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    12. Götz Alefeld & Zhengyu Wang, 2011. "Error Bounds for Nonlinear Complementarity Problems with Band Structure," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 33-51, July.
    13. Li, Qiang & Li, Yongxiang, 2015. "Monotone iterative technique for second order delayed periodic problem in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 654-664.
    14. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    15. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    16. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    17. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    18. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    19. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    20. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:111:y:2004:i:2:p:317-354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.