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Update StoCal_Defs.md
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Fubini's theorem
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mxcfb authored Oct 9, 2021
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Expand Up @@ -129,7 +129,7 @@ In particular,

let $X_{t}=\int_{0}^{t} \alpha_{s} d W_{s}$ be the Ito integral of $\alpha$ with respect to a Brownian motion $W$ and $\mathbb{E}(\int_{0}^{t} \alpha_{s}^{2} d s)<\infty$ for all $t \geq 0$, then
$$
\mathbb{E}\left(X_{t}^{2}\right)=X_{0}^{2}+\mathbb{E}\left(\int_{0}^{t} \alpha_{s}^{2} d s\right)=\mathbb{E}\left(\int_{0}^{t} \alpha_{s}^{2} d s\right).
\mathbb{E}\left(X_{t}^{2}\right)=X_{0}^{2}+\mathbb{E}\left(\int_{0}^{t} \alpha_{s}^{2} d s\right)=\mathbb{E}\left(\int_{0}^{t} \alpha_{s}^{2} d s\right)=\int_{0}^{t} \mathbb{E}(\alpha_{s}^{2}) d s.
$$


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