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 real 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}