Journal of Mathematical Sciences

, Volume 76, Issue 1, pp 2163–2168 | Cite as

Convergence rate estimates in some limit theorems for maximum random sums

  • V. Yu. Korolev
  • D. O. Selivanova
Article

Abstract

Some estimates of the accuracy of the approximation of the distribution of maximum partial random sums by the distribution of the maximum of the standard Wiener process are given in the case of an asymptotically degenerate index.

Keywords

Convergence Rate Limit Theorem Rate Estimate Wiener Process Standard Wiener Process 

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References

  1. 1.
    V. Yu. Korolev, “Convergence of random sequences with independent random indices,” {jtTeor. Veroyatn. Primen.}, {vn39}, {snNo. 2} ({dy1994}).Google Scholar
  2. 2.
    V. M. Kruglov and V. Yu. Korolev,Limit Theorems For Random Sums [in Russian], Moscow Univ. Press, Moscow (1990).Google Scholar
  3. 3.
    C. C. Heyde and J. R. Leslie, “On moment measures of departure from the normal and exponential laws,”Stoch. Proc. Appl.,4, 317–328 (1976).CrossRefMathSciNetGoogle Scholar
  4. 4.
    P. Hall, “On measures of the distance of a mixture from its parent distribution,”Stoch. Proc. Appl.,8, 357–365 (1979).CrossRefMATHGoogle Scholar
  5. 5.
    V. Paulauskas, “On the sum of a random number of random vectors,”Litovskii Mat. Sb.,12, No. 2, 109–131 (1972).MATHMathSciNetGoogle Scholar
  6. 6.
    V. Yu. Korolev, “On the accuracy of the normal approximation to distributions of sums of a random number of independent random variables,”Teor. Veroyatn. Primen.,33, No. 3, 577–581 (1988).MATHMathSciNetGoogle Scholar
  7. 7.
    T. V. Arak, “On the distributions of maxima of cumulative sums of independent random variables,”Teor. Veroyatn. Primen.,19, No. 2, 257–277 (1974).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. Yu. Korolev
    • 1
  • D. O. Selivanova
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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