= Multitype Poisson branching process
{title2=$B_i(\Lambda)$}
A particle of type $i$ has independently a <Poisson distribution> of type-$j$ offspring with <mean> $\lambda_{ij}$. Different particles reproduce independently. If $p^{(t)}_i$ is the <probability> generation $t$ is nonempty from one type-$i$ ancestor, then $p^{(0)}=\mathbf1$ and $p^{(t+1)}=T(p^{(t)})$, where $T_i(x)=1-\exp[-(\Lambda x)_i]$. This iteration decreases to the <survival probability of a branching process>, the greatest nonnegative <fixed point> of $T$. The expected type-count row <vector> in generation $t$ is $e_i^T\Lambda^t$.
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