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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

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conditional expectation brownian motion

$B=(B_t,t\in[0,1])$ a standard brownian motion on $[0,1]$. For $t\in[0,1]$, we define $$\mathcal{F}_t=\sigma(B_s,s\in[0,t]),$$ $$\mathcal{G}_t=\mathcal{F}_t\,\vee\,\sigma(B_1).$$ How can we show $$\ …
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