Dambis-Dubins-Schwarz theorem
= Dambis-Dubins-Schwarz theorem
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Let $M$ be a continuous local martingale with $M_0=0$ and $[M]_\infty=\infty$. For
$$
\tau_s=\inf\{t\geq0:[M]_t>s\},
$$
the process $B_s=M_{\tau_s}$ is <Brownian motion> and
$$
M_t=B_{[M]_t}.
$$
When $[M]_\infty<\infty$, one can enlarge the probability space and continue $B$ independently beyond that time.
= Dubins-Schwarz theorem
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