The Kolmogorov Equation is a fundamental concept in probability theory and stochastic processes. It describes how the probability distribution of a system changes over time, particularly in systems influenced by random events. This equation is essential for understanding processes like diffusion and population dynamics. In its most common form, the Kolmogorov Forward Equation provides a way to calculate the future state of a system based on its current state and transition rates. Conversely, the Kolmogorov Backward Equation focuses on how past states influence the present. Together, these equations form the backbone of many models in fields such as finance, physics, and biology.