Let $T_1, T_2, T_3, \, \ldots \overset{d}{=} \text{Exponential}(1)$ each be a
D4000: Standard exponential random positive real number such that
A
D6135: Random unsigned real process $X : [0, \infty) \to \text{Random}(\Omega \to [0, \infty))$ is a
standard real poisson process if and only if
\begin{equation}
\forall \, t \in [0, \infty) :
X_t
\overset{d}{=} \max \left\{ N \in \mathbb{N} : \sum_{n = 1}^N T_n \leq t \right\}
\end{equation}
