Let $X_t$ be a strict local martingale and let $S$ and $T$ be stopping times with $S \leq T$. Prove that $[X]_S=[X]_T$ implies that $X_t$ is almost surely constant on $[S, T]$, where $[X]_S$ and $[X]_T$ is the quadratic variation of the stopped process.
Quadratic variation and stopping time.
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stochastic-processes
stopping-times
quadratic-variation