Calculus on random integral mappings $I_{(a,b]}^{h,r}$ and their domains

Abstract

It is proved that the random integral mappings (some type of functionals of Lévy processes) are always isomorphisms between convolution semigroups of infinitely divisible measures. However, the inverse mappings are no longer of the random integral form. Domains are characterized in may ways. Compositions (iterated integrals) can be expressed as a single random integral mapping. Finally, all obtained results are illustrated by examples.

References in corpus (1)

• A class of multivariate infinitely divisible distributions related to arcsine density

Cited by in corpus (1)

• Remarks on factorization property of some stochastic integrals