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Poissonian Processes
A Poissonian Process is one governed by Poisson Statistics.
Mathematical Formulation
$$\mathcal{POIS}(\mathbf{X}=x; \lambda) = \frac{\lambda^{x}e^{-\lambda}}{x!}$$
With the $n$-th sampling from this distribution being noted: $\mathbf{X}_n \thicksim \mathcal{POIS}(\mathbf{X}=x; \lambda)$