 Dambis-Dubins-Schwarz theorem

Let $M$ be a continuous local martingale with $M_0=0$ and $[M{]}_{\infty }=\infty$. Forthe process $B_s=M_{{\tau }_s}$ is Brownian motion andWhen $[M{]}_{\infty }<\infty$, one can enlarge the probability space and continue $B$ independently beyond that time.