Compositions of some random integral mappings (and a conjecture)

Seminar | August 28 | 3:10-4 p.m. | 1011 Evans Hall

 Zbigniew J. Jurek, University of Wroclaw

 Department of Statistics

In the 1980's, the Lévy class L of self-decomposable distributions was characterized as distributions of some special random integrals.
That led to more general theory applied to other classes of distributions. Random integral mappings (some type of functionals of Lévy processes) are continuous homomorphisms between
convolution sub-semigroups of ID (the semigroup of all infinitely divisible measures). We will show that compositions of those random integrals (mappings) can be always expressed as
another single random integral mapping. That fact is illustrated by some old (Thorin class T) and new examples of distributions (free infinite divisibility).

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