The survival probability of a weakly subcritical multitype branching process in iid random environment

We study the asymptotic behavior of the probability of non extinction of a weakly subcritical multitype branching process in iid random environments. Under suitable assumptions, the survival probability is of order of ${\rho }^n{n}^{-3\mathrm{/}2}$ for some $\rho \in (0,1)$ to specify.