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. Acknowledgement: Financial support of this work comes in part from NSF under grant ANI-0338856. The author is grateful to P. Chainais and J. Barral for stimulating discussions and to P. Chainais and D. Gershman for providing some of the figures. Infinitely Divisible Shot-Noise: Cascades of Non-Compact Pulses Rudolf H. Riedi Dept. of Statistics, Rice University, Houston, Texas School of Engineering and Architecture, Fribourg, Switzerland