Markov jump processes and collision-like models in the kinetic description of multi-agent systems

TL;DR

This paper explores the relationship between Markov jump processes and collision-like models in kinetic descriptions of multi-agent systems, enhancing understanding by linking two different modeling approaches.

Contribution

It establishes a formal connection between Markov jump processes and collision-like models, enabling the transfer of analytical techniques between these frameworks.

Findings

Demonstrates the parallelism between the two models

Provides methods to analyze kinetic jump process models using collisional techniques

Enhances the theoretical understanding of multi-agent system dynamics

Abstract

Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in the spirit of the classical kinetic approach in gas dynamics, but also as Markov jump processes, which assume that every agent is stimulated by the other agents to change state according to a certain transition probability distribution. In this paper we establish a parallelism between these two descriptions, whereby we show how the understanding of the kinetic jump process models may be improved taking advantage of techniques typical of the collisional approach.