If $B$ is a Brownian-motion in the $\mathcal{F}$ filtration, then the following process is a good example for being a local martingale, but not a martingale?$$S_{t}=\int_{0}^{t}\frac{1}{1-s}dB_{s},\;\;\;t\in\left[0,1\right)$$
2026-02-23 06:21:48.1771827708
Is it a good example for local martingale, but not for martingale?
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