Diffusion of Brownian particles governed by fluctuating friction

The problem of diffusion of Brownian particles is revisited under the condition of fluctuactions of the Stokes friction, which depends on the viscosity of the medium surrounding the Brownian particle, as well as on its shape and size. Various classes of discontinuous and continuous stochastic processes describing fluctuating friction are considered. All these cases lead to normal diffusion. The diffusion constant, however, deviates from the usual Einstein form: in particular it generically depends on the Brownian particle's mass. For all considered cases it is a decreasing function of mass.