Tails of bivariate stochastic recurrence equation with triangular matrices

10/09/2021

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by   Ewa Damek, et al.

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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.