Minimising the time to a decision

Book English OPEN
Jacka, Saul D. ; Warren, Jon ; Windridge, Peter (2011)
  • Publisher: University of Warwick. Centre for Research in Statistical Methodology
  • Subject: QA

Suppose we have three independent copies of a regular diffusion on [0,1] with\ud absorbing boundaries. Of these diffusions, either at least two are absorbed at the\ud upper boundary or at least two at the lower boundary. In this way, they determine\ud a majority decision between 0 and 1. We show that the strategy that always runs\ud the diffusion whose value is currently between the other two reveals the majority\ud decision whilst minimising the total time spent running the processes.
  • References (21)
    21 references, page 1 of 3

    [1] R. Cairoli and R. C. Dalang. Sequential stochastic optimization. Wiley Series in Probability and Statistics: Probability and Statistics. John Wiley & Sons Inc., New York, 1996. A Wiley-Interscience Publication.

    [2] R. Cairoli and J. B. Walsh. Stochastic integrals in the plane. Acta Math., 134:111- 183, 1975.

    [3] L. Chaumont and R. A. Doney. Some calculations for doubly perturbed Brownian motion. Stochastic Process. Appl., 85(1):61-74, 2000.

    [4] L. Chaumont, R. A. Doney, and Y. Hu. Upper and lower limits of doubly perturbed brownian motion. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 36(2):219 - 249, 2000.

    [5] R. A. Doney and T. Zhang. Perturbed Skorohod equations and perturbed reflected diffusion processes. Ann. Inst. H. Poincar´e Probab. Statist., 41(1):107-121, 2005.

    [6] N. El Karoui and I. Karatzas. Dynamic allocation problems in continuous time. Annals of Applied Probability, 4(2):255-286, 1994.

    [7] N. El Karoui and I. Karatzas. Synchronization and optimality for multi-armed bandit problems in continuous time. Mat. Apl. Comput., 16(2):117-151, 1997.

    [8] J. Gittins and D. Jones. A dynamic allocation index for the sequential design of experiments. In J. Gani, editor, Progress in Statistics, pages 241-266. North-Holland, Amsterdam, NL, 1974.

    [9] L. Hu and Y. Ren. Doubly perturbed neutral stochastic functional equations. J. Comput. Appl. Math., 231(1):319-326, 2009.

    [10] K. Itoˆ and H. P. McKean, Jr. Diffusion processes and their sample paths. SpringerVerlag, Berlin, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 125.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    9
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    Warwick Research Archives Portal Repository - IRUS-UK 0 9
Share - Bookmark