Occupation-times formula
= Occupation-times formula
For a continuous semimartingale $X$ with <local time of a semimartingale> $L_t^a(X)$,
$$
\int_0^tf(X_s)d[X]_s=\int_{\mathbb R}f(a)L_t^a(X)da
$$
for every nonnegative measurable function $f$.
= Occupation-times formula
For a continuous semimartingale $X$ with <local time of a semimartingale> $L_t^a(X)$,
$$
\int_0^tf(X_s)d[X]_s=\int_{\mathbb R}f(a)L_t^a(X)da
$$
for every nonnegative measurable function $f$.