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Carthaginian enlargement of filtrations

Giorgia Callegaro, Monique Jeanblanc, Behnaz Zargari (2013)

ESAIM: Probability and Statistics

This work is concerned with the theory of initial and progressive enlargements of a reference filtration 𝔽 F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an 𝔽 F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable...

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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