= Itô formula for semimartingales with jumps
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For a <semimartingale> with <càdlàg> paths $X$ and $f\in C^2$, the <Itô formula> uses the left-limit gradient in $\int f'(X_{s-})dX_s$, the continuous <quadratic variation> in its second-order integral, and the jump correction $\sum_{s\leq t}[f(X_s)-f(X_{s-})-f'(X_{s-})\Delta X_s]$. In several dimensions use the corresponding gradient, Hessian and continuous bracket matrix. The correction is the part of each jump not captured by first-order linearization.
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