New answers tagged metric-spaces
3
votes
Accepted
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 ...
- 31.5k
3
votes
Accepted
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{...
- 78.3k
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(...
- 505
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