Random Series with Time-Varying Discounting

被引：0
|
作者：
Donchev, Doncho S. [1 ]
机构：
[1] Sofia Univ St Kliment Ohridski, Fac Math & Informat, Sofia, Bulgaria
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2011年 / 40卷 / 16期
关键词：
GARCH(1,1) and ARCH processes; Mellin transform; Meyer G-functions; Stochastic recurrence equations; EQUATION;
D O I：
10.1080/03610926.2011.562772
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 xi(1), xi(2), ... be i.i.d. non negative random variables. Consider the series 1 + Sigma(infinity)(n=1) Pi(n)(i=1) xi(i). It turns out that its partial sums are equal to some random determinants. This allows us to represent the original series as an infinite product of random variables that form a Markov chain. The limit behavior of the series depends on the stationary distribution of this chain. Making use of the Mellin transform, we study the relationship between this distribution and the distribution of xi(1).
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页码：2866 / 2878
页数：13
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