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
Topological space
Continuous map
Continuous function
Right-continuous function
Almost surely right-continuous random function
Cadlag random function
Lévy process
Standard real Wiener process
Definition D3657
Real Wiener process
Formulation 4
Let $B : [0, \infty) \to \text{Random}(\mathbb{R})$ be a D3658: Standard real Wiener process.
A D5076: Random real process $W : [0, \infty) \to \text{Random}(\mathbb{R})$ is a Wiener process with parameters $\mu \in \mathbb{R}$ and $\sigma \in (0, \infty)$ if and only if \begin{equation} \forall \, t \in [0, \infty) : W_t \overset{d}{=} \mu t + \sigma B_t \end{equation}
Results
Distribution of the real Wiener process at a given point is gaussian