Year: 2008
Type: article
Abstract: A random vector $X$ with representation $X=∑_{j≥0}A_jZ_j$ 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.
Source: Bernoulli
DOI: 10.3150/08-bej125
Authors: Henrik Hult, Gennady Samorodnitsky
Institutions: Brown University, Cornell University
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2006030430