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1 vote

Does this distribution exist?

Denote $f(t) = \frac{\sin t}{t}$. Then your identity is that for any $u,v\in\mathbb{R}^2$, $$ \frac{\hat W(u) \hat W(v)}{\hat W(u+v)} = f(u\times v) $$ Therefore, for any $u,v,w\in\mathbb{R}^2$, $$ \...
user49822's user avatar
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3 votes

Does this distribution exist?

It seems your equation implies $\hat{W}(0,\mu_1)\hat{W}(0,\mu_2)=\hat{W}(0,\mu_1+\mu_2)$, which would mean that $\hat{W}(0,\mu)= e^{c\mu}$. This is not the Fourier transform of a valid marginal ...
Carlo Beenakker's user avatar
1 vote

Lipschitz approximation of a probability measure with finite $1$-st moment by the ones with finite $p$-th moment

$\newcommand{\R}{\mathbb R}$This is only a partial answer in the sense that it will provide $\frac 1p$-Hölder maps, not Lipschitz. I still hope it can help. Fix a big radius $R>0$ (I like $R\to\...
leo monsaingeon's user avatar

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