Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 202 / 3 / a / Solution

Write the $d$-dimensional continuous semimartingale as $X=X_0+M+A$, where $M$ is a continuous local martingale and $A$ is a continuous finite-variation process. For $f\in C^2({\mathbb{R}}^d)$, Itô formula states