Can someone tell me, where I can find a proof of the following fact:
Let $M$ be a continuous local martingale with $M_0=0$. Then we have $ P \left(\max_{s \leq t} \; M_s \geq y, \ [M]_t \leq C \right) \leq \exp \left(-\frac{y^2}{2C} \right) $ for every $t, y, C> 0$.
Here I denote by $[M]_t$ the quadratic variation of $M$.