Is there any (non trivial) continuous non negative martingale which converges to 0?
2026-04-07 02:48:23.1775530103
Continuous Non negative martingale converging to 0
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Sure, try $M_t=B_{t\wedge T}$ where $(B_t)$ is a Brownian motion starting from $B_0=1$ and $T$ is the first hitting time of $0$ by $(B_t)$.