Feynman-Kac theorem

The Feynman-Kac theorem connects certain types of differential equations with the expected outcomes of random processes, specifically stochastic (random) paths. In essence, it shows that solving a complex equation describing, for example, how a price evolves over time, can be done by averaging the results of many simulated random trajectories—like stock prices fluctuating unpredictably. This allows us to use probability and simulation techniques to find solutions to problems in physics, finance, and engineering, turning difficult mathematical equations into more manageable calculations based on the expected behavior of random systems.