The unified Ito formula has the pseudo-Poisson structure df(x)=[f(x+b)−f(x)]μνdaνμ
V. P. Belavkin · Journal of Mathematical Physics · 1993
A universal functional Ito formula, recently discovered within the *-Ito noncommutative algebraic approach, is described herein. The formula unifies the classical Ito formulas for Wiener, Poisson, and quantum cases, extends the chain rule df(x1,...,xl) = ∑f′i(x)dxi to the case of noncommuting stochastically differentiable operators Xi(t), and also admits a nonadapted generalization.