If $(N_t)_{t \in \mathbb{R}_+}$ is a point process (or a Poisson process), what does it mean $$ N_t - N_{t-} \in \{ 0, 1 \}? $$ Notation: $N_{t-} = \underset{u \rightarrow t^-}{lim} N_u$.
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2026-03-26 16:04:09.1774541049
A question involving Poisson processes
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It may just mean that in an infinitesimal amount of time (say $dt$) you can only have at most one arrival. In other words, the probability of more than one arrival in a small interval $dt$ is negligible.