Kolmogorov equations

In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize random dynamic processes.

In order to try to explain them in simple ideas, suppose we have a complete statistical description of a stochastic process x(t) and know some transformation,a function of the stochastic variable, (for example, velocity, which is the derivative of the state variable) which defines a new process y(t) related to x(t), for the velocity example :. Then the Kolmogorov equations are a means for determining features of the stochastic process y(t), thus without needing to know the stochastic process itself, the details.