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Conditions for convergence of random coefficient AR(1) processes and perpetuities in higher dimensions
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
2014 (English)In: Bernoulli, ISSN 1350-7265, Vol. 20, no 2, 990-1005 p.Article in journal (Refereed) Published
Abstract [en]

A d-dimensional RCA(1) process is a generalization of the d-dimensional AR(1) process, such that the coefficients {M-t; t =1, 2, ...} are i.i.d. random matrices. In the case d =1, under a nondegeneracy condition, Goldie and Mailer gave necessary and sufficient conditions for the convergence in distribution of an RCA(1) process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition parallel to Pi(n)(t=1) M-t parallel to -greater than(a.s.) 0 as n -greater than infinity, most of the results of Goldie and Mailer can be extended to the case d greater than 1. If this condition does not hold, some of their results cannot be extended.

Place, publisher, year, edition, pages
Bernoulli Society for Mathematical Statistics and Probability , 2014. Vol. 20, no 2, 990-1005 p.
Keyword [en]
AR(1) process; convergence; higher dimensions; matrix norm; matrix product; perpetuity; random coefficient; random difference equation; random matrix; RCA(1) process
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-106115DOI: 10.3150/13-BEJ513ISI: 000333440800022OAI: diva2:714051
Available from: 2014-04-25 Created: 2014-04-24 Last updated: 2014-05-15

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Erhardsson, Torkel
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Mathematical Statistics The Institute of Technology
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