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

Yuri P. Virchenko and M. I. Yastrubenko

Abstract and Applied Analysis, 2006, vol. 2006, 1-12

Abstract:

The integral limit theorem as to the probability distribution of the random number ν m of summands in the sum ∑ k = 1 ν m ξ k is proved. Here, ξ 1 , ξ 2 , … are some nonnegative, mutually independent, lattice random variables being equally distributed and ν m is defined by the condition that the sum value exceeds at the first time the given level m ∈ ℕ when the number of terms is equal to ν m .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:056367

DOI: 10.1155/AAA/2006/56367

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