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Abstract and Applied Analysis
Volume 2006, Article ID 56367, 12 pages

The integral limit theorem in the first passage problem for sums of independent nonnegative lattice variables

Belgorod State University, Pobedy 85, Belgorod 308015, Russia

Received 26 June 2005; Accepted 1 July 2005

Copyright © 2006 Yuri P. Virchenko and M. I. Yastrubenko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The integral limit theorem as to the probability distribution of the random number νm of summands in the sum k=1νmξk is proved. Here, ξ1,ξ2, are some nonnegative, mutually independent, lattice random variables being equally distributed and νm is defined by the condition that the sum value exceeds at the first time the given level m when the number of terms is equal to νm.