ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
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▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
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▼ Measurable space
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▼ Independent event collection
▼ Independent collection of event collections
▼ Independent collection of sigma-algebras
▼ Independent random collection
▼ I.I.D. random collection
▼ Strong white noise random real collection
Definition D5292
Standard strong white noise random real collection
Formulation 0
A D5291: Random real collection $X : J \to \text{Random}(\mathbb{R})$ is a standard strong 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) $X$ is an D3358: I.I.D. random collection