Change search
ReferencesLink to record
Permanent link

Direct link
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

Open Access in DiVA

fulltext(269 kB)74 downloads
File information
File name FULLTEXT01.pdfFile size 269 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Erhardsson, Torkel
By organisation
Mathematical Statistics The Institute of Technology
In the same journal
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 74 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 108 hits
ReferencesLink to record
Permanent link

Direct link