SpringerLink
Log in

On Generalizations of the Optimal Choice Problem

  • MATHEMATICS
  • Published:
Vestnik St. Petersburg University, Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we consider generalizations of the optimal choice problem. There is a sequence of n identically distributed random variables on the interval [0, 1]. Sequentially obtaining the observed values of these quantities, it is necessary at some point to stop at one of them, taking it as the starting point for counting the upper or lower record values. In the optimal choice problem and its generalizations, it is required to make the correct choice of the starting point of the records in order to maximize the mathematical expectation of the sum of values or the number of upper, lower, or both record values obtained as a result of such a procedure. A review of the results on the uniform distribution of random variables and new results on the exponential distribution of random variables are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Spain)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. Gardner, “Mathematical Games. A fifth collection of "brain-teasers”,” Sci. Am. 202, 150–154 (1960).

    Article  Google Scholar 

  2. E. B. Dynkin, “Optimal choice of the stop** time of a Markov process,” Soviet Math. Dokl. 4, 627–629 (1963).

    MATH  Google Scholar 

  3. V. B. Nevzorov and S. A. Tovmasyan, “On the maximal value of the expectation of record numbers,” Vestn. St. Petersburg Univ.: Math. 47, 64–67 (2014). https://doi.org/10.3103/S1063454114020046

    Article  MathSciNet  MATH  Google Scholar 

  4. I. V. Bel’kov and V. B. Nevzorov, “On the problem of the optimal choice of record values,” Vestn. St. Petersburg Univ.: Math. 51, 107–113 (2018). https://doi.org/10.3103/S1063454118020024

    Article  MathSciNet  Google Scholar 

  5. I. V. Bel’kov and V. B. Nevzorov, “On one problem of the optimal choice of record values,” J. Math. Sci. 244, 718–722 (2020). https://doi.org/10.1007/s10958-020-04644-0

    Article  MathSciNet  MATH  Google Scholar 

  6. I. V. Bel’kov, “On some tasks of optimal selection of record values,” Nauchn. Zh. «Globus», No. 11 (44), 46–49 (2019).

Download references

Funding

The study was supported by the Russian Foundation for Basic Research, project no. 18-01-00393.

Author information

Authors and Affiliations

  1. St. Petersburg State University, 199034, St. Petersburg, Russia

    I. V. Belkov

Authors
  1. I. V. Belkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Belkov.

Additional information

Translated by A. Ivanov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belkov, I.V. On Generalizations of the Optimal Choice Problem. Vestnik St.Petersb. Univ.Math. 54, 22–27 (2021). https://doi.org/10.1134/S1063454121010052

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063454121010052

Keywords:

Search

Navigation