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Lipschitz-regularity of partition of unity

For convenience write $$ \phi_U(x) = \| x - (K-U)\|. $$ Let $N = |\mathcal{U}|$ the number of open sets in the cover. Define $$ f_1(x) = \frac{1}{N} \sum \phi_U(x), \qquad f_2(x) = \left( \frac1N \sum ...
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3 votes
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Linear process close to a Gaussian process

$\newcommand{\R}{\mathbb R}\newcommand{\Z}{\mathbb Z}\newcommand{\ep}{\varepsilon}\newcommand{\de}{\delta}$Let $\psi_j:=0$ for $j=-1,-2,\dots$. Then \begin{equation*} X_t=\sum_{j\in\Z}X_{t,j} \end{...
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3 votes

Linear process close to a Gaussian process

The definition of a Gaussian process is as follows. A stochastic process $X(t), t \in T $ is a Gaussian process if for all $n \in \mathbb{N}$, $a_i \in \mathbb{R}$, $t_i \in T$, $\sum_{i=1}^n a_i X(...
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