Markov evolutions and hierarchical equations in the continuum: II. Multicomponent systems

TL;DR

This paper develops evolution equations for multicomponent particle systems in the continuum, focusing on birth-death and hopping dynamics, and establishes conditions for analyzing these equations in Banach spaces.

Contribution

It introduces a framework for deriving and analyzing evolution equations for multicomponent systems with complex stochastic dynamics in the continuum.

Findings

Derived evolution equations for quasi-observables and correlation functions.

Provided sufficient conditions for the equations to be well-posed in Banach spaces.

Extended the mathematical understanding of multicomponent stochastic particle systems.

Abstract

General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We also present sufficient conditions that allows us to consider these equations on suitable Banach spaces.