Siberian Advances in Mathematics

, Volume 28, Issue 4, pp 303–308 | Cite as

Inequalities for Functions of the Sum of the Indicators of Events

  • A. S. TarasenkoEmail author


We obtain moment inequalities for the sum of the indicators of events and an upper estimate for a convex function of such a sum. Our results generalize inequalities that were obtained earlier for moment characteristics of the sojourn time of a random walk on a half-axis.


moment inequalities sum of indicators 


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  1. 1.
    A. N. Borodin and I. A. Ibragimov, “Limit theorems for functionals of random walks,” TrudyMat. Inst. Steklov 195, 3 (1994) [Proc. Steklov Inst. Math. 195, 1 (1995)].Google Scholar
  2. 2.
    W. Feller, An introduction to Probability Theory and its Applications. Vol. 2 (John Wiley and Sons, New York, 1971).zbMATHGoogle Scholar
  3. 3.
    C. Jordan, Calculus of Finite Differences (Chelsea Publishing Company, New York, 1965).zbMATHGoogle Scholar
  4. 4.
    V. I. Lotov, “Asymptotic expansions for the distribution of the sojourn time of a random walk on a half-axis,” Trudy Mat. Inst. Steklov 282, 154 (2013) [Proc. Steklov Inst. Math. 282, 146 (2013)].MathSciNetzbMATHGoogle Scholar
  5. 5.
    V. I. Lotov and A. S. Tarasenko, “On the asymptotics of the mean sojourn time of a random walk on a semiaxis,” Izv. Ross. Akad. Nauk, Ser. Mat. 79, No. 3, 23 (2015) [Izv. Math. 79, 449 (2015)].MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    A. V. Skorokhod and N. P. Slobodenyuk, Limit Theorems for Random Walks (Naukova Dumka, Kiev, 1970) [in Russian].zbMATHGoogle Scholar
  7. 7.
    F. Spitzer, Principles of Random Walk (Springer, New York, 2001).zbMATHGoogle Scholar
  8. 8.
    A. S. Tarasenko, “Inequalities for the sojourn time of random walks above a certain boundary,” Sib. Elektron. Mat. Izv. 13, 434 (2016) [in Russian].MathSciNetzbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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