Stable Systems with Power Law Conditions for Poisson Hail

TL;DR

This paper analyzes Poisson hail models to identify critical conditions ensuring system stability, including cases with infinite propagation speed, providing insights into the behavior of such stochastic systems.

Contribution

It characterizes stability conditions for Poisson hail models, especially under infinite speed of propagation, advancing understanding of their critical moments.

Findings

Identifies critical moments for stability

Characterizes stability boundaries in Poisson hail models

Includes analysis of infinite propagation speed case

Abstract

We consider Poisson hail models and characterize up to boundaries the collection of critical moments which guarantee stability. In particular, we treat the case of infinite speed of propagation.