Show that, in Theorem 19.17, the quadratic variation \(\langle Mangle_{t}\) is a \(\mathscr{G}_{t}\) stopping time.Direct calculation, use Lemma 19.16.c) and A. 15

Data From Theorem 19.17

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19.17 Theorem (Doeblin 1940; Dambis 1965; Dubins-Schwarz 1965). Let (Mt, Ft)t20, M+ L(P), be a continuous martingale with a right continuous filtration, i.e. F = Ft+, t> 0, and (M) = limt-00 (M) = 00. Denote by T = inf{t > 0 (M)t > s} the generalized inverse of (M). Then (Bt, Gt)t20 := (MTF)so is a Brownian motion, and Mt B(M) for all t 0.