What is Ito's lemma?

What is Ito's lemma?

Approach: State formula for stochastic differential.

For Ito process dX_t = μ_t dt + σ_t dW_t and function f(t,X_t), df = (∂f/∂t + μ_t ∂f/∂x + ½σ_t² ∂²f/∂x²)dt + σ_t ∂f/∂x dW_t.

Follow-up: Apply to f(W_t)=W_t².

Key concepts: stochastic differential, quadratic variation, Ito calculus.