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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Yu. Korolev, “Convergence of random sequences with independent random indices,” {jtTeor. Veroyatn. Primen.}, {vn39}, {snNo. 2} ({dy1994}).
V. M. Kruglov and V. Yu. Korolev,Limit Theorems For Random Sums [in Russian], Moscow Univ. Press, Moscow (1990).
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).
P. Hall, “On measures of the distance of a mixture from its parent distribution,”Stoch. Proc. Appl.,8, 357–365 (1979).
V. Paulauskas, “On the sum of a random number of random vectors,”Litovskii Mat. Sb.,12, No. 2, 109–131 (1972).
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).
T. V. Arak, “On the distributions of maxima of cumulative sums of independent random variables,”Teor. Veroyatn. Primen.,19, No. 2, 257–277 (1974).
Author information
Authors and Affiliations
Additional information
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993.
Rights and permissions
About this article
Cite this article
Korolev, V.Y., Selivanova, D.O. Convergence rate estimates in some limit theorems for maximum random sums. J Math Sci 76, 2163–2168 (1995). https://doi.org/10.1007/BF02363229
Issue Date:
DOI: https://doi.org/10.1007/BF02363229