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1 results

  • On an optimal selection problem of Cowan and Zabczyk

  • F. Thomas Bruss
  • Journal:
    Journal of Applied Probability / Volume 24 / Issue 4 / December 1987
    Published online by Cambridge University Press:
    14 July 2016, pp. 918-928
    Print publication:
    December 1987

  • Cowan and Zabczyk (1978) have studied a continuous-time generalization of the so-called secretary problem, where options arise according to a homogeneous Poisson processes of known intensity λ. They gave the complete strategy maximizing the probability of accepting the best option under the usual no-recall condition. In this paper, the solution is extended to the case where the intensity λ is unknown, and also to the case of an inhomogeneous Poisson process with intensity function λ (t), which is either supposed to be known or known up to a multiplicative constant.