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The inner characterization of geometric stable laws. (English) Zbl 0923.60020

Summary: A geometric stable law is defined as a limiting distribution of appropriately normalized sums of a random number of i.i.d. random variables, where the number of terms has a geometric distribution. We investigate the stability property of such laws and give the inner characterization of this class. The explicit representation of normalizing constants for distributions in the domain of attraction of a geometric stable law is also provided.

MSC:

60E07 Infinitely divisible distributions; stable distributions
60G50 Sums of independent random variables; random walks
60F05 Central limit and other weak theorems
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