Given a filtration $(\mathcal{F}_n)_{n\geq 0}$ and a stopping time $T$, show that there exists an adapted process $(X_n)_{n\geq 0}$ such that $$T=\inf \{n \geq 0 : X_n >0\}$$
I'm really lost where to even begin here, any help would be appreciated.
Given a filtration $(\mathcal{F}_n)_{n\geq 0}$ and a stopping time $T$, show that there exists an adapted process $(X_n)_{n\geq 0}$ such that $$T=\inf \{n \geq 0 : X_n >0\}$$
I'm really lost where to even begin here, any help would be appreciated.
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