Convergence of two-dimensional branching recursions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:130

Article

Cramer, M ; Rüschendorf, L

关键词: branching type recursion;    contraction method;    random matrices;   

DOI  :  10.1016/S0377-0427(99)00391-X

来源: Elsevier

【 摘 要 】

The asymptotic distribution of branching type recursions (L-n) of the form L-n =(d) A Ln-1 + B (L) over bar (n-1) is investigated in the two-dimensional case. Here (L) over bar (n-1) is an independent copy of (L) over bar (n-1) and A,B are random matrices jointly independent of (L) over bar (n-1),(L) over bar (n-1). The asymptotics of L-n 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. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

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