Solution
= Solution
The <Dambis-Dubins-Schwarz theorem> states that if $M$ is a <continuous local martingale> with $M_0=0$ and $[M]_\infty=\infty$, then, for
$$
\tau_s=\inf\{t\geq0:[M]_t>s\},
$$
the process $W_s=M_{\tau_s}$ is a standard <Brownian motion> and $M_t=W_{[M]_t}$. If $[M]_\infty<\infty$, one obtains the same representation after enlarging the <probability space> and continuing $W$ independently beyond $[M]_\infty$.