Skip to main content
SpringerLink
Log in

On One Problem of the Optimal Choice of Record Values

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Independent random variables X1, X2, . . . , Xn having U([0, 1])-uniform distribution and upper record values in this set are considered. We study the problem of maximizing (taking into account some consecutively observed values x1, x2, . . . , xk of these X’s) the expectation of sums of records in this sequence under the optimal choice of the corresponding variable Xk (instead of X1) as the initial record value.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records, Wiley, New York (1998).

    Book  Google Scholar 

  2. M. Ahsanullah and V. B. Nevzorov, Records via Probability Theory, Atlantis Press (2015).

  3. V. B. Nevzorov, Records. Mathematical Theory [in Russian], Moscow (2000).

  4. M. Gardner, “Mathematical Games. A fifth collection of ‘brain-teasers’,” Sci. Amer., 202, 150–154 (1960).

    Article  Google Scholar 

  5. E. B. Dynkin. “Optimal choice of the stopping moment of a Markov process,” Dokl. Akad. Nauk SSSR, 150, 238–240 (1963).

    MathSciNet  Google Scholar 

  6. S. M. Gusein-Zade, Fastidious Bride [in Russian], Moscow (2003).

  7. 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).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    I. V. Bel’kov & V. B. Nevzorov

Authors
  1. I. V. Bel’kov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. B. Nevzorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Bel’kov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 30–37.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bel’kov, I.V., Nevzorov, V.B. 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-020-04644-0

Search

Navigation