= Cox process
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{title2=$N\mid\Lambda\sim\operatorname{Poisson\ process}(\Lambda)$}
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= Doubly-stochastic Poisson process
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A counting process which, conditional on a random nonnegative locally integrable intensity $\Lambda$, is an <Inhomogeneous Poisson process>. For $L_t=\int_0^t\Lambda(s)\,ds$, conditioning gives $\mathbb EN(t)=\mathbb EL_t$ and $\operatorname{Var}N(t)=\mathbb EL_t+\operatorname{Var}L_t$. Thus finite-variance counts are never underdispersed. Randomness of the intensity may induce dependence between increments which are independent conditionally.
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