Modeling of a non-stationary trajectories ensemble using Fokker-Planck equation

There is Discusses the kinetic Fokker-Planck equation for sample density distribution functions of random variables seen in practice in the form of the time number. Instead of studying one of the possible realizations of the time series it is proposed to consider an ensemble of random trajectories generated by the empirical distribution function. A model is proposed to describe the time variation functional defined on random trajectories and practical importance. This, for example, the indicator of level of pollution of the metropolis in the form of average pollutant concentration over a certain period of time, a similar indicator of the changing epidemiology in the region, the functional efficiency in the management of pollution in the form of lower pollution levels as a result of certain actions, etc. There is formulated a method of testing the control functions for the non-stationary trajectories ensemble.