Stationarity of multivariate particle systems

TL;DR

This paper investigates the conditions under which multivariate particle systems remain stationary over time, providing characterizations especially for multivariate Brown-Resnick processes, enhancing understanding of their temporal behavior.

Contribution

It offers new conditions and a full characterization of stationarity for multivariate particle systems, including Brown-Resnick processes.

Findings

Conditions for stationarity in multivariate particle systems

Full characterization of stationary multivariate Brown-Resnick processes

Enhanced understanding of temporal properties of these processes

Abstract

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation of the stationarity property. In particular, a full characterisation of stationary multivariate Brown-Resnick processes is given.