  A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ 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.
