Poisson-Vlasov : Stochastic representation and numerical codes

TL;DR

This paper introduces a stochastic representation involving exponential and branching processes for solving the Poisson-Vlasov equation with multiple charged species, offering insights into solution behavior and a new numerical evaluation method.

Contribution

It presents a novel stochastic approach for representing solutions to the Poisson-Vlasov equation, facilitating both analysis and numerical computation.

Findings

Provides a stochastic representation involving exponential and branching processes.

Offers an intuitive understanding of solution fluctuations.

Proposes a new numerical method based on the stochastic representation.

Abstract

A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization of the nature of the solutions and its fluctuations. Here, the stochastic representation is also proposed as a tool for the numerical evaluation of the solutions