Convergence of two-dimensional branching recursions

Abstract The asymptotic distribution of branching type recursions (Ln) of the form L n = d A L n−1 +B L n−1 is investigated in the two-dimensional case. Here L n−1 is an independent copy of Ln−1 and A,B are random matrices jointly independent of L n−1 , L n−1 . The asymptotics of Ln after normalization are derived by a contraction method. The limiting distribution is characterized by a fixed point equation. The assumptions of the convergence theorem are checked in some examples using eigenvalue decompositions and computer algebra.

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