stochastic chain rule

[stō′kas·tik ′chān ‚rül] (mathematics) 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 ^α dW ^β= ∂_αβ dt, where the X ⁱare processes satisfying {W_t^α, t ≥ 0}, α = 1, 2, … , m, are independent Wiener processes; the dW_t^αare the corresponding random disturbances occurring in the infinitesimal time interval dt ; the a_tⁱand b_t^{i α}are independent of future disturbances, and u (x₁, x₂, …, x_n) is a function whose derivatives ∂_i u and ∂_i∂_j u are continuous. Also known as Itô's formula.

单词	stochastic chain rule
释义	stochastic chain rule stochastic chain rule [stō′kas·tik ′chān ‚rül] (mathematics) 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 ^α dW ^β= ∂_αβ dt, where the X ⁱare processes satisfying {W_t^α, t ≥ 0}, α = 1, 2, … , m, are independent Wiener processes; the dW_t^αare the corresponding random disturbances occurring in the infinitesimal time interval dt ; the a_tⁱand b_t^{i α}are independent of future disturbances, and u (x₁, x₂, …, x_n) is a function whose derivatives ∂_i u and ∂_i∂_j u are continuous. Also known as Itô's formula.
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