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edited Oct 16, 2015 at 1:45

Bjørn Kjos-Hanssen

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If $X∼F1$X∼F_1$,Y∼F2$ $Y∼F_2$, under what conditions on $F1$F_1$,F2$ are needed s.t. we $F_2$ can we construct $Y=E(X|\mathscrX\mid\mathscr{G})$ for some $\mathscr{G}$?

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asked Oct 16, 2015 at 0:18

Anthony Lee Zhang

If $X∼F1,Y∼F2$, what conditions on $F1,F2$ are needed s.t. we can construct $Y=E(X|\mathscr{G})$ for some $\mathscr{G}$?

Suppose that we have distributions $F_1 $ and $F_2$. Under what conditions on $F_1,F_2$ is it possible to construct random variables $X\sim F_1,Y\sim F_2$ such that $Y=E(X|\mathscr{G})$, that is, $Y$ is the conditional expectation of $X$ with respect to some $\sigma$-field $\mathscr{G}$?

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