Kolmogorov backward equations (diffusion)

The Kolmogorov backward equation (KBE) and its adjoint, the Kolmogorov forward equation, are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931.^[1] Later it was realized that the forward equation was already known to physicists under the name Fokker–Planck equation; the KBE on the other hand was new.