Tails of bivariate stochastic recurrence equation with triangular matrices

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-know...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 150; pp. 147 - 191
Main Authors Damek, Ewa, Matsui, Muneya
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2022
Subjects
Autoregressive models
Kesten’s theorem
Regular variation
Stochastic recurrence equation
Triangular matrix
secondary
Kesten’s theorem
Triangular matrix
Stochastic recurrence equation
Autoregressive models
Regular variation
primary
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2022.04.008