On the decomposition of infinitely divisible probability laws without normal factor

Warped infinitely divisible cascades: beyond power laws

We address the definitions and synthesis of stochastic processes which possess warped scaling laws that depart from power law behaviors in a controlled manner. We define warped infinitely divisible cascading (IDC) noise, motion and random walk. We provide a theoretical derivation of the scaling behavior of the moments of their increments. We provide numerical simulations of a warped log-Normal ...

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.

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...