We study properties of a p-type subcritical branching process in random environment initiated at moment zero by a vector z = (z1,.., zp) of particles of different types. For p = 1 the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment n behaves as C(z)λn for large n, where the parameters λ ∈ (0, 1) and C(z) ∈ (0, ∞) are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment n → ∞ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process.
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