Stochastic order and attractiveness for particle systems with multiple births, deaths and jumps

TL;DR

This paper develops a general method to compare complex particle systems with births, deaths, and jumps using transition rate inequalities, providing explicit couplings and conditions for attractiveness, with applications to various models.

Contribution

It offers a unified characterization of stochastic order and attractiveness for a broad class of interacting particle systems, including explicit coupling constructions.

Findings

Characterization of stochastic order via transition rate inequalities

Explicit coupling construction for particle systems

Improved ergodicity results for epidemic models

Abstract

An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We give a characterization of stochastic order between different interacting particle systems in a large class of processes with births, deaths and jumps of many particles per time depending on the configuration in a general way: it consists in checking inequalities involving the transition rates. We construct explicitly the coupling that characterizes the stochastic order. As a corollary we get necessary and sufficient conditions for attractiveness. As an application, we first give the conditions on examples including reaction-diffusion processes, multitype contact process and conservative dynamics and then we improve an ergodicity result for an epidemic model.