Integration with respect to the G-Brownian local time

Let LL be the local time of G-Brownian motion B  . In this paper, we consider the existence of the quadratic covariation 〈f(B),B〉t〈f(B),B〉t and the integral ∫Rf(x)L(dx,t)∫Rf(x)L(dx,t). Under some suitable conditions we show that the sublinear version of the Bouleau–Yor identity∫Rf(x)L(dx,t)=−〈f(B),B〉t holds. These allow us to write the Itô formula for C1C1-functions.