Infinitely Divisible Cylindrical Measures on Banach Spaces

Second quantisation for skew convolution products of measures in Banach spaces∗

We study measures in Banach space which arise as the skew convolution product of two other measures where the convolution is deformed by a skew map. This is the structure that underlies both the theory of Mehler semigroups and operator selfdecomposable measures. We show how that given such a set-up the skew map can be lifted to an operator that acts at the level of function spaces and demonstra...

Cylindrical Lévy processes in Banach spaces

Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and hence weak (cylindrical) stochastic processes. In this paper we focus on cylindrical Lévy processes. These have (weak) Lévy-Itô decompositions and an associa...

Representation of infinitely divisible distributions on cones

We investigate infinitely divisible distributions on cones in Fréchet spaces. We show that every infinitely divisible distribution concentrated on a normal cone has the regular Lévy–Khintchine representation if and only if the cone is regular. These results are relevant to the study of multidimensional subordination.

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Infinitely Divisible Shot-Noise: Cascades of Non-Compact Pulses

Recently, the concept of infinitely divisible scaling has attracted much interest. As models of this scaling behavior, Poisson products of Cylindrical Pulses and more general infinitely divisible cascades have been proposed. This paper develops path and scaling properties of Poisson products of arbitrary pulses with non-compact support such as multiplicative and exponential shot-noise processes...