Limit theorems for a multi-type Galton-Watson process in random independent environment

Abstract : The theory of multi-type branching process in i.i.d. environment is considerably less developed than for the univariate case, and fundamental questions are up to date unsolved. Answers demand a deep understanding of the behaviour of products of i.i.d. matrices with non-negative entries. Under mild assumptions, when the probability generating functions of the reproduction laws are fractional-linear, the survival probability of the multi-type branching process in random environment up to moment n is proportional to 1/√n as n → ∞. Techniques for univariate branching processes in random environment and methods from the theory of products of i.i.d. random matrices are required.
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Submitted on : Friday, December 7, 2018 - 2:46:55 PM
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Thi da Cam Pham. Limit theorems for a multi-type Galton-Watson process in random independent environment. Probability [math.PR]. Université de Tours, 2018. English. ⟨tel-01948215⟩

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