A generalization of the ordinary chain rule to stochastic processes; it states that the process U_t = u(X_t¹, X_t², ..., X_tⁿ) satisfies

with the conventions (dt )² = 0 and dW ^αdW ^β = ∂_αβdt, where the Xⁱ are processes satisfying

are independent Wiener processes; the dW_t^α are the corresponding random disturbances occurring in the infinitesimal time interval dt; the a_tⁱ and b_t^iα are independent of future disturbances, and u(x₁, x₂, ..., x_n ) is a function whose derivatives ∂_iu and ∂_i∂_ju are continuous. Also known as Itô's formula.