Ito's lemma
Ito's lemma is a fundamental result in stochastic calculus that provides a way to find the differential of a function of a stochastic process. It is particularly useful for processes that follow Brownian motion, allowing us to apply calculus to random variables. Essentially, it extends the chain rule from traditional calculus to accommodate the randomness inherent in stochastic processes.
The lemma states that if you have a function of a stochastic process, you can express its change in terms of the process's change and its derivatives. This is crucial for fields like finance, where it helps in modeling the dynamics of asset prices and in the pricing of derivatives.