Chapman-Kolmogorov Equation

The Chapman-Kolmogorov equation is a fundamental principle in probability theory that helps us calculate the likelihood of transitioning from one state to another over multiple steps. Essentially, it states that the probability of moving from an initial state to a final state can be found by summing over all possible intermediate states, multiplying the probabilities of moving through each step. This allows us to analyze complex systems, like weather patterns or stock markets, by breaking down their future behavior into simpler, consecutive transitions, making the overall process easier to understand and predict.