1 Kolmogorov Equations
In Probability Theory, the 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;
- The Kolmogorov backward equation for continuous processes; and
- The Kolmogorov backward equation for jump processes.
These important results have a discrete analogue known as the Chapman-Kolmogorov Equations for Markov Chains.