Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and (tau) a stopping time. Find (leftlangle B^{tau}ightangle_{t}).

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Let \(\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}\) be a \(\mathrm{BM}^{1}\) and \(\tau\) a stopping time. Find \(\left\langle B^{\tau}ightangle_{t}\).

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