On infinitely divisible semimartingales

Infinitely Divisible Cylindrical Measures on Banach Spaces

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Furthermore, continuity properties and the relation to infinitely...

Infinitely Divisible Matrices

Infinitely divisible cascades

Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. It was recently shown and explained how and why multifractal analysis could be interestingly and fruitfully placed in the more general framework of infinitely divisible cascades. The aim of this contribution is to design processes, c...

On Exact Scaling Log-infinitely Divisible Cascades

In this paper we extend some classical results valid for canonical multiplicative cascades to exact scaling log-infinitely divisible cascades. We complete previous results on non-degeneracy and moments of positive orders obtained by Barral and Mandelbrot, and Bacry and Muzy: we provide a necessary and sufficient condition for the non-degeneracy of the limit measures of these cascades, as well a...

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.