A stochastic representation for the Poisson-Vlasov equation
  A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence proof and an intuitive characterization of the solutions, may also be used to obtain an intrinsic definition of the fluctuations. 
R. Vilela Mendes and Fernanda Cipriano