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 support of this work comes in part from NSF under grants ANI-0338856 and VIGRE0240058, and from Sony Instruments. The principal author is grateful to P. Chainais for stimulating discussions and for providing some of the plots in figure 1. Infinitely Divisible Shot-Noise: Modeling Fluctuations in Networking and Finance Rudolf H. Riedi and Darrin Gershman Dept. of Statistics, Rice University, Houston, Texas Abstract. 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.