ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5289
Strong white noise random real collection
Formulation 0
A D5291: Random real collection $X : J \to \text{Random}(\mathbb{R})$ is a strong white noise random real collection if and only if
(1) \begin{equation} \forall \, j \in J : \mathbb{E} X_j \in \mathbb{R} \end{equation}
(2) \begin{equation} \forall \, j \in J : \text{Var} X_j \in (0, \infty) \end{equation}
(3) $X$ is an D3358: I.I.D. random collection
Also known as
Strong sense white noise random real collection
Children
▶ D5292: Standard strong white noise random real collection
▶ D1296: Weak white noise random real collection