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Optimal rules for the sequential selection of monotone subsequences of maximum expected length

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  • Bruss, F. Thomas
  • Delbaen, Freddy

Abstract

This article presents new results on the problem of selecting (online) a monotone subsequence of maximum expected length from a sequence of i.i.d. random variables. We study the case where the variables are observed sequentially at the occurrence times of a Poisson process with known rate. Our approach is a detailed study of the integral equation which determines v(t), the expected number (under the optimal strategy for time horizon t) of selected points Ltt up to time t. We first show that v(t), v'(t) and v''(t) exist everywhere on . Then, in particular, we prove that v''(t)

Suggested Citation

  • Bruss, F. Thomas & Delbaen, Freddy, 2001. "Optimal rules for the sequential selection of monotone subsequences of maximum expected length," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 313-342, December.
    • Handle: RePEc:eee:spapps:v:96:y:2001:i:2:p:313-342
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    Cited by:

    1. Bruss, F. Thomas & Delbaen, Freddy, 2004. "A central limit theorem for the optimal selection process for monotone subsequences of maximum expected length," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 287-311, December.
    2. Arlotto, Alessandro & Nguyen, Vinh V. & Steele, J. Michael, 2015. "Optimal online selection of a monotone subsequence: a central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3596-3622.
    3. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    4. Gnedin, Alexander & Seksenbayev, Amirlan, 2021. "Diffusion approximations in the online increasing subsequence problem," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 298-320.

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