A Note on the Convolution of Probability Measures

On infinite divisibility and embedding of probability measures on a locally compact Abelian group

In the present note the authors supplement significant properties of infinitely divisible and embeddable probability measures on a locally compact Abelian group G. There are at least two versions of infinite divisibility appearing in the literature which deserve special attention, and the problem of embedding those measures leads directly to the study of continuous convolution semigroups on G. ...

A note on the comparison between Laplace and Sumudu transforms

Computing moments of free additive convolution of measures

This short note explains how to use ready-to-use components of symbolic software to convert between the free cumulants and the moments of measures without sophisticated programming. This allows quick access to low order moments of free convolutions of measures, which can be used to test whether a given probability measure is a free convolution of other measures.

Multiplication of free random variables and the S-transform: the case of vanishing mean

This note extends Voiculescu’s S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the S-transform in the case of vanishing mean, the usual formula makes perfectly good sense.

Short Note on Inf-Convolution Preserving the Fatou Property

We model agents’ preferences by cash-invariant concave functionals defined on L∞, and formulate the optimal risk allocation problem as their infimal-convolution. We study the case of agents whose choice functionals are law-invariant with respect to different probability measures and show how, in this case, the value function preserves a desirable dual representation (equivalent to the Fatou pro...