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Tail probabilities for infinite series of regularly varying random vectors
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Mathematical Statistics)ORCID iD: 0000-0001-9210-121X
Cornell University, ORIE.
2008 (English)In: Bernoulli, ISSN 1350-7265, Vol. 14, no 3, 838-864 p.Article in journal (Refereed) Published
Abstract [en]

A random vector X with representation X = Sigma(j >= 0)A(j)Z(j) is considered. Here, (Z(j)) is a sequence of independent and identically distributed random vectors and (A(j)) is a sequence of random matrices, 'predictable' with respect to the sequence (Z(j)). The distribution of Z(1) is assumed to be multivariate regular varying. Moment conditions on the matrices (A(j)) are determined under which the distribution of X is regularly varying and, in fact, 'inherits' its regular variation from that of the (Z(j))'s. We compute the associated limiting measure. Examples include linear processes, random coefficient linear processes such as stochastic recurrence equations, random sums and stochastic integrals.

Place, publisher, year, edition, pages
2008. Vol. 14, no 3, 838-864 p.
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-81927DOI: 10.3150/08-BEJ125ISI: 000264166300012OAI: diva2:497767
Swedish Research Council
QC 20120307Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-03-07Bibliographically approved

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