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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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