ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Measure space
Probability space
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 D1296
Weak white noise random real collection
Formulation 0
A D5291: Random real collection $X : J \to \text{Random}(\mathbb{R})$ is a weak 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) \begin{equation} \forall \, i, j \in J \left( i \neq j \quad \implies \quad \text{Cov}(X_i, X_j) = 0 \right) \end{equation}
Children
Standard weak white noise random real collection