  In a recent paper Calogero and Alcantara derived a Lorentz-invariant
Fokker-Planck equation, which corresponds to the evolution of a particle
distribution associated with relativistic Brownian Motion. We study the "one
and one-half" dimensional version of this problem with nonlinear
electromagnetic interactions - the relativistic Vlasov-Maxwell-Fokker-Planck
system - and obtain the first results concerning well-posedness of solutions.
Specifically, we prove the global-in-time existence and uniqueness of classical
solutions to the Cauchy problem and a gain in regularity of the distribution
function in its momentum argument.
