Markov dynamics on the cone of discrete Radon measures

TL;DR

This paper explores Markov dynamics on the space of discrete Radon measures, extending known results from configuration spaces to these more general measure spaces, with applications to models like contact, Bolker--Dieckmann--Law--Pacala, and Glauber dynamics.

Contribution

It introduces Markov dynamics on discrete Radon measures and adapts existing configuration space results to this broader context.

Findings

Developed analogues of contact, Bolker--Dieckmann--Law--Pacala, and Glauber dynamics for discrete Radon measures

Extended known configuration space results to measure spaces of Radon measures

Provided a framework for analyzing stochastic processes on measure spaces

Abstract

We start with a brief overview of the known facts about the spaces of discrete Radon measures those may be considered as generalizations of configuration spaces. Then we study three Markov dynamics on the spaces of discrete Radon measures: analogues of the contact model, of the Bolker--Dieckmann--Law--Pacala model, and of the Glauber-type dynamics. We show how the results obtained previously for the configuration spaces can be modified for the case of the spaces of discrete Radon measures.