Abstract
We investigate a multi-type Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Suppose that the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices has negative mean and assuming some additional conditions, we find the asymptotics of the survival probability at time $n$ as $n \to \infty$.
Highlights
Branching processes in random environment are natural generalization of simple Galton-Watson processes
A branching process in random environment was first considered by Smith and Wilkinson (11)
A lot of papers is devoted to the study of the survival probability of single-type branching processes in random environment (see, for example, (1)-(9))
Summary
On subcritical multi-type branching process in random environment. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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