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Key words: infinitely divisible distribution; the Goldie-Steutel-Bondesson class; stochastic inte- gral mapping; compound Poisson process; limit of the ranges of the iterated
The purpose of this work is to study the free infinitely divisible laws (FGGC) corresponding to the image of Λ of classical Generalized Gamma Convolutions and their corresponding
Theorem 1 of [5] gives concentration bounds for a class of infinitely divisible laws with finite exponential moments, and in the compound Poisson case it reduces precisely to (5),
Our interest in the questions considered in this paper was sparked by a related, but apparently more difficult, problem concerning coalescing L´evy processes on the circle that
In Section 3 we give some simple examples of how to use Theorems 1.1 and 1.2 to estimate the expected value of the norm of Hilbert space valued infinitely divisible random variables
We prove that for symmetric Markov processes of diffusion type admitting a “carré du champ”, the Poincaré inequality is equivalent to the exponential convergence of the
This would have finished off the problem of characterizing Gaussian random variables with infinitely divisible squares and, more significantly, by (1.3), would show that when a
The aim of this paper is to propose a new kind of matrix ensembles; between classically and freely infinitely divisible laws connected through the Bercovici- Pata bijection,
