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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, ...

Adapted from math stack exchange. Background: the prototypical example of---and way to generate---smooth noise is by convolving a one-dimensional white noise process with a Gaussian kernel. My ...

$\DeclareMathOperator\erf{erf}$ Let's consider the Gaussian distribution $P_X(x)= \frac{1}{\sqrt{2 \pi \sigma^2}} e^{- \frac{x^2}{2 \sigma^2}}$. Now consider the random variable $W \equiv \max \{ X_1, ...

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 ...

Suppose I have two independent random variables $X$, $Y$, each modeled by the Gaussian mixture model (GMM). That is, $$ f(x)=\sum _{k=1}^K \pi _k \mathcal{N}\left(x|\mu _k,\sigma _k\right) $$ $$ g(y)=\...