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Geometric infinite divisibility, stability, and self-similarity: an overview

Tomasz J. Kozubowski — 2010

Banach Center Publications

The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of N p components for each p ∈ (0,1), where N p is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....

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