A Generalized Occupation Time Formula For Continuous Semimartingales

Raouf Ghomrasni

We show that for a wide class of functions $F$ that: $$ {\lim_{ε\downarrow 0} {\frac{1}ε} \int_0^t \Big\{F(s, X_s) - F(s, X_s - ε)\Big\} d\big<X,X\big>_s} = - \int_0^t\int_{\R} F(s…