We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions ${\bf W} =(W_1,W_2)$. 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.
翻译：我们用三角矩阵系数研究双轨重复式复发方程式,并用三角矩阵系数来描述其固定解决方案的尾部行为 $_bf W} = (W_1,W_2) = (W_1,W_2) = (W_1,W_2) 。 最近发现, $W_ 1,W_2美元 可能以不同指数定期显示不同的尾部, 这与众所周知的 Kesten 类型结果不同。 但是, 仅得出部分结果 。 在典型的“ Kesten- Goldie” 和“ Grey” 条件下, 我们完全描述尾部行为 $W_ 1,W_2美元 = (W_1,W_2) = (W_2) 。 在先前的随机复发方程式环境中, 我们所发现的尾部无效方程式没有观察到。
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