Inhomogeneous Poisson process (source code)

= Inhomogeneous Poisson process
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An inhomogeneous Poisson process with locally integrable intensity $\lambda(t)\geq0$ has independent increments and
$$
N_t-N_s\sim\operatorname{Poisson}\left(\int_s^t\lambda(u)\,du\right)
$$
for $0\leq s<t$. Its cumulative intensity is $\Lambda(t)=\int_0^t\lambda(u)\,du$.