Tails of bivariate stochastic recurrence equation with triangular matrices

Ewa Damek and Muneya Matsui

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 147-191

Abstract: We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions W=(W1,W2). Recently it has been observed that W1,W2 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 W1,W2. The tail asymptotics we obtain has not been observed in previous settings of stochastic recurrence equations.

Keywords: Stochastic recurrence equation; Regular variation; Kesten’s theorem; Autoregressive models; Triangular matrix (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.008

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