Weak convergence of mutually independent and under weak convergence of
W. Szczotka (2006)
Applicationes Mathematicae
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For each n ≥ 1, let and be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let , , t ≥ 0, and . The main result gives conditions under which the weak convergence , where X is a Lévy process, implies and , where and are mutually independent Lévy processes and .