ThmDex – An index of mathematical definitions, results, and conjectures.
F9109
Formulation 0
A D5291: Random real collection $X : J \to \text{Random}(\mathbb{R})$ is a standard weak white noise random real collection if and only if
(1) \begin{equation} \forall \, j \in J : \mathbb{E} X_j = 0 \end{equation}
(2) \begin{equation} \forall \, j \in J : \text{Var} X_j = 1 \end{equation}
(3) \begin{equation} \forall \, i, j \in J \left( i \neq j \quad \implies \quad \text{Cov}(X_i, X_j) = 0 \right) \end{equation}