Vlasov scaling for stochastic dynamics of continuous systems

TL;DR

This paper introduces a general method for deriving Vlasov-type equations for Markov particle systems in continuous space, using a scaling of generators and hierarchical correlation functions, with practical examples.

Contribution

It presents a novel, systematic scheme for deriving Vlasov equations for continuum particle systems via generator scaling and hierarchical correlation functions.

Findings

The scheme applies to various Markov models of particle systems.

It provides an algorithmic way to obtain Vlasov equations.

Examples demonstrate the approach's versatility.

Abstract

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.