Itô's lemma for the Itô drift-diffusion process d X t = μ μ t d t + σ σ t d B t says that the differential of a twice-differentiable function f (t, x) is given by d f = ( ∂ ∂ f ∂ ∂ t + μ μ t ∂ ∂ f ∂ ∂ x + σ σ t 2 2 ∂ ∂ 2 f ∂ ∂ x 2 ) d t + σ σ t ∂ ∂ f ∂ ∂ x d B t .