Kolmogorov equations

In probability theory, Kolmogorov equations characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time. There are four distinct equations: the Kolmogorov forward equation for continuous processes, now understood to be identical to the Fokker–Planck equation, the Kolmogorov forward equation for jump processes, and two Kolmogorov backward equations for processes with and without discontinuous jumps.