Large deviation rates for supercritical multitype branching processes with immigration

Liuyan Li, Junping Li

Let $\{X_n{\}}_{n\ge 0}$ be a $p$-type ($p\ge 2$) supercritical branching process with immigration and mean matrix $M$. Suppose that $M$ is positively regular and $\ddot{I}$ is the maximal…