Tails of bivariate stochastic recurrence equation with triangular matrices
Tails of bivariate stochastic recurrence equation with triangular matrices
复制标题
三角矩阵二元随机递推方程的尾部
DOI：
10.1016/j.spa.2022.04.008
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发表时间：
2022
影响因子：
1.4
通讯作者：
Ewa Damek and Muneya Matsui
中科院分区：
文献类型：
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作者：
Shih Jia-Han;Konno Yoshihiko;Chang Yuan-Tsung;Emura Takeshi;Ewa Damek and Muneya Matsui
我们研究了具有三角矩阵系数的二元随机递推方程，并描述了它们的平稳解W=(w1, w2)的尾部行为。最近已经观察到w1， w2在不同的指数下可能表现出规律变化的尾部，这与众所周知的kesten型结果相反。然而，只得到了部分结果。在典型的“Kesten-Goldie”和“Grey”条件下，我们完全描述了w1、w2的尾部行为。我们得到的尾部渐近性在以前的随机递归方程设置中没有观察到。
We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions W=(W 1, W 2). Recently it has been observed that W 1, W 2 may exhibit regularly varying tails with different indices, which is in contrast to well-known Kesten-type results. However, only partial results have been derived. Under typical “Kesten–Goldie” and “Grey” conditions, we completely characterize tail behavior of W 1, W 2. The tail asymptotics we obtain has not been observed in previous settings of stochastic recurrence equations.