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.
A new technique for finding conservation laws of partial differential equations
The Structure of Lie Algebras and the Classification Problem for Partial Differential Equations
On the different types of global and local conservation laws for partial differential equations in three spatial dimensions: review and recent developments
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