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Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications. (English) Zbl 1120.60033

Summary: This paper uses a new method to achieve some new equivalent conditions on asymptotics and local asymptotics for random sums, modifies some results based on an incorrect lemma, and cancels some technical conditions on the existing corresponding results. The newly obtained equivalent conditions are applied to risk theory and infinite divisibility theory, and some new results are derived.

MSC:

60F99 Limit theorems in probability theory
60E07 Infinitely divisible distributions; stable distributions
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