Consider two i.i.d. random variable $X$ and $Y$. Suppose I know the characteristic function of $Z=X-Y$ (say $\phi_{(X-Y)}$) can I recover the characteristic function $\phi_{(X)}$ ? I know that if I had the characteristic function of $X+Y$ then $\phi_{(X+Y)} = \phi_{(X)} \cdot \phi_{(Y)} \equiv \phi_{(X)}^2 $ which means I can recover $()$ but am not sure if that is doable from $\phi_{(X-Y)}$ without further assumptions (say symmetry). Ideas?
2026-04-01 07:22:40.1775028160
Recover component characteristic function from from difference of i.i.d. random variables...
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