Optional time-change theorem
= Optional time-change theorem
Let $M$ be a <continuous local martingale> and let $(\tau_s)$ be an increasing continuous family of finite <stopping times>. Under the usual compatibility conditions, $M_{\tau_s}$ is a continuous local martingale for the time-changed filtration $\mathcal F_{\tau_s}$. A finite-variation process remains of finite variation after the same time change.