Generalized Fokker–Planck equation for non-Markovian processes

This paper deals with a system of linear non-Markovian–Langevin equations with memory functions that are not constant in time and a nonzero initial instant of time. A set of statistical means, based on the application of a generalized Furutsu–Novikov formula, was used to derive a generalized Fokker–Planck equation corresponding to this system and holding for both long and short instants of time. Considered as an example is the Brownian motion of a particle in a viscoelastic fluid with a particular relaxation time.