Alternative description of stochastic processes in nonlinear systems. “Kinetic form” of master and Fokker-Planck equations

An alternative description of stochastic processes in nonlinear systems is considered. It is shown that among the possible forms of the Fokker-Planck and the Langevin equations (Ito, Stratonovich, and kinetic forms) the kinetic form is more natural from the point of view of the statistical theory. A new form of the master equation for one-step processes is proposed which is in agreement with the kinetic form of the Fokker-Planck equation. Some concrete examples are considered.