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Just how regular are the sample paths of 1D white noise smoothed with a Gaussian kernel?
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 ...
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Existence of unique convolution semigroups of probability measures on more general spaces then $\mathbb R^d$
Let $E$ be a $\mathbb R$-Banach space, $\mathcal M_1(E)$ (resp. $\mathcal M_1^\infty(E)$) denote the set of probability measures (resp. infinitely divisible probability measures) on $E$, $\varphi_\mu$ ...
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