A general approach to sample path generation of infinitely divisible processes via shot noise representation

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...

Infinitely Divisible Shot-Noise: Modeling Fluctuations in Networking and Finance

This paper provides an introduction to recent advances in the study of scale-invariance and related phenomena, namely the concept of infinitely divisible scaling which encompasses statistical self-similarity and multifractal scaling. Further the paper develops path properties and scaling of Poisson products of multiplicative and exponential shot-noise processes. Acknowledgement: Financial suppo...

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

Log-infinitely divisible multifractal processes

We define a large class of multifractal random measures and processes with arbitrary loginfinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson “product of cynlindrical pulses” [7]. Their construction involves some “continuous stochastic m...

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.