Itô formula

For an Itô process $d{X}_t=b_{t}dt+{\sigma }_{t}d{B}_t$ and a twice differentiable function $f$,The second-order term reflects the nonzero quadratic variation of Brownian motion.

For a continuous semimartingale $X$,where $L^0(X)$ is the local time of a semimartingale at zero.

Local time measures how intensely a semimartingale visits a level. For a continuous semimartingale it appears as the increasing correction term in the Tanaka formula.