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post: typo fix
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Locietta committed May 1, 2024
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10 changes: 3 additions & 7 deletions posts/possibility-calculation.md
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Expand Up @@ -615,13 +615,9 @@ $\{M_n\}$是关于$\{X_n\}$的**鞅**,$T$是$\{M_n\}$的一个**停时**,那
2. $E(T)<\infin$,并且$E(|M_{n+1}-M_n|)\leq c < \infin$
3. $P(T\leq \infin)=1$,并且$M_{T\wedge n} \leq K < \infin$

:::info NOTE

OST的成立条件其实就是在问$M_T$是否**一致可积**,也就是能否**交换积分和极限的顺序**。如果答案是肯定的,那么显然就有

$$
E(M_{0}) = \lim_{n\to\infin}E(M_{T\wedge n})=E\left(\lim_{n\to\infin}M_{T\wedge n}\right)=E(M_T)
$$
> [!note]
> OST的成立条件其实就是在问$M_{T\wedge n}$是否**一致可积**,也就是能否**交换积分和极限的顺序**。如果答案是肯定的,那么显然就有
> $$E(M_{0}) = \lim_{n\to\infin}E(M_{T\wedge n})=E\left(\lim_{n\to\infin}M_{T\wedge n}\right)=E(M_T)$$
:::

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