(Existence and uniqueness for (4.10)). Generalize the existence and uniqueness theorem and the localization principle, given in Section 4.7, for the system (4.10).
The stochastic differential equation (4.1) can be interpreted in the Stratonovich sense by making the integral in (4.2) a Stratonovich integral; that is, by writing it in the form
To convert in the other direction; that is, from Itô form to Stratonovich form, the Wong–Zakai correction is subtracted. Thus, the Itô equation dx = a(x, t) dt + b(x, t) dw is converted to the equivalent Stratonovich form