Convergence to a process with independent increments in a scheme of increasing sums of dependent random variables

This article derives conditions under which a sequence of random set functions on subsets of a finite-dimensional space constructed in terms of increasing sums of dependent nonnegative random variables converges (in the sense of convergence of finite-dimensional distributions) to a random set function with independent increments which have infinitely divisible distributions. The results obtained are applied to the problem of the number of long repetitions in a sequence of trials.
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