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

preprint2013arXivOpen access

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.

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

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Calculus on random integral mappings I(a,b]h,rI^{h,r}_{(a,b]}I(a,b]h,r​ and their domains

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