Journal of Mathematical Sciences

, Volume 244, Issue 5, pp 718–722 | Cite as

On One Problem of the Optimal Choice of Record Values

  • I. V. Bel’kovEmail author
  • V. B. Nevzorov

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.


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  1. 1.
    B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records, Wiley, New York (1998).CrossRefGoogle Scholar
  2. 2.
    M. Ahsanullah and V. B. Nevzorov, Records via Probability Theory, Atlantis Press (2015).Google Scholar
  3. 3.
    V. B. Nevzorov, Records. Mathematical Theory [in Russian], Moscow (2000).Google Scholar
  4. 4.
    M. Gardner, “Mathematical Games. A fifth collection of ‘brain-teasers’,” Sci. Amer., 202, 150–154 (1960).CrossRefGoogle Scholar
  5. 5.
    E. B. Dynkin. “Optimal choice of the stopping moment of a Markov process,” Dokl. Akad. Nauk SSSR, 150, 238–240 (1963).MathSciNetGoogle Scholar
  6. 6.
    S. M. Gusein-Zade, Fastidious Bride [in Russian], Moscow (2003).Google Scholar
  7. 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).MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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