On tails of fixed points of the smoothing transform in the boundary case

被引：22
作者：
Buraczewski, Dariusz [1 ]
机构：
[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2009年 / 119卷 / 11期
关键词：
Smoothing transform; Branching random walk; Distributional equations; Random difference equation; BRANCHING RANDOM-WALK;
D O I：
10.1016/j.spa.2009.09.005
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let {A(i)} be a sequence of random positive numbers, such that only N first of them are strictly positive, where N is a finite a.s. random number. In this paper we investigate nonnegative solutions of the distributional equation Z =(d)Sigma(N)(i=l) A(i)Z(i), where Z, Z(1), Z(2), .... are independent and identically distributed random variables, independent of N, A(1), A(2), ... . We assume E[Sigma(N)(i=1) A(i)] = 1 and E[Sigma(N)(i=1) A(i) log A(i)] = 0 (the boundary case), then it is known that all nonzero solutions have infinite mean. We obtain new results concerning behavior of their tails. (C) 2009 Elsevier B.V. All rights reserved.
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收藏
页码：3955 / 3961
页数：7
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