伊藤の補助定理と構文分析

I can see some resemblance between Ito's lemma and the chain rule, as both provide a means to solve for the derivative of a function of a variable that is itself a function of a second variable with respect to that second variable.
e.g. df(x(t))/dt = (df/dx)(dx/dt) in the case of chain rule.
However, while the chain rule is straightforward to derive from the definition of x, Ito's lemma does not seem so simple to derive from the drift diffusion process X. i.e. It does not seem so simple to find df(X(t),t)/dt given
X(t) = mu(t)+sigma(t)*dB(t)/dt

Another area of confusion continues to be the need for different parsing algorithms. I do not see why compilers cannot simply use the CYK algorithm for syntactic analysis and augment the parse tree derived by this algorithm for use in semantic analysis. I am not sure that the complexity of algorithms like LR is better than the O(n^3*|G|) complexity of CYK.