All Questions

Let $\varphi(x)=\frac{1}{\sqrt{2\pi}}\exp(-x^2/2)$ be the Gaussian density and $f:\mathbb{R}\to\mathbb{R}$ another measurable function. Under what conditions can $f$ be recovered from its convolution ...

In the book Gaussian Measures in Finite and Infinite Dimensions by Stroock, there is a theorem with a comment The following remarkable theorem was discovered by Cramér and Lévy. So far as I know, ...

Suppose $X$ is a random variable with a density $f(x)$ such that $f(x)$ is a convolution of some density $g$ with some other density $q$: $$ f = g\ast q. $$ Under what conditions does $X=h(Y)$, where $...