1&=&E[X_t]=E[E[X_t|\mathcal{F}_{t\wedge T_b}]]=E[X_{t\wedge T_b}]\\&=&E[X_t1_{\{t<T_b\}}]+E[X_{T_b}1_{\{t\geq T_b\}}]
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  4. http://mkprob.hatenablog.com/entry/2013/11/07/000227
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