A note on randomly scaled scale-decorated Poisson point processes

2018/02/13 by Bhattacharya, Ayan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.04842

Abstract

Randomly scaled scale-decorated Poisson point process is introduced recently in Bhattacharya et al. [2017] where it appeared as weak limit of a sequence of point processes in the context of branching random walk. In this article, we obtain a characterization for these processes based on scaled-Laplace functional. As a consequence, we obtain a characterization for strictly α-stable point process (also known as scale-decorated Poisson point process) based on scaled-Laplace functional . a connection with randomly shifted decorated Poisson point process is obtained. The tools and approach used e very similar to those in Subag and Zeitouni [2015].

Related

• Branching-stable point processes
• The range of a self-similar additive gamma process is a scale invariant Poisson point process
• Extremal behavior of stationary marked point processes
• Scaling limits of branching random walks and branching stable processes
• Branching Random Walks, Stable Point Processes and Regular Variation