  In this work we recast the collisional Vlasov-Maxwell and Vlasov-Poisson
equations as systems of coupled stochastic and partial differential equations,
and we derive stochastic variational principles which underlie such
reformulations. We also propose a stochastic particle method for the
collisional Vlasov-Maxwell equations and provide a variational characterization
of it, which can be used as a basis for a further development of stochastic
structure-preserving particle-in-cell integrators.
