Ito's Formula

Ito's Formula is a fundamental tool in stochastic calculus used to find how a function of a random process evolves over time. It's similar to the chain rule in regular calculus but adapted for processes that have unpredictable, jumpy behavior, like stock prices. The formula accounts for both the usual change in the process and the variability or “noise” inherent in it. Essentially, Ito's Formula allows us to track and predict the behavior of functions influenced by randomness, making it essential in finance, physics, and other fields dealing with uncertain systems.