Kolmogorov Equations

Kolmogorov equations are mathematical tools used to describe how probabilities change over time in systems that evolve randomly, such as particles moving unpredictably or stock prices fluctuating. There are two types: the forward equation (Fokker-Planck) predicts how the probability distribution of a system's state develops, while the backward equation helps analyze expected future outcomes based on current conditions. These equations help scientists model and understand complex stochastic processes by providing a way to track the evolving likelihood of different states in a systematic manner.