Abstract
Consider the series ∑n C n Z n where {Z n} are iid -valued random vectors and {C n} are random matrices independent of the {Z n}. Under suitable summability conditions on the {C n}, if the distribution of Z 1 is multivariate regularly varying at oo then so is the distribution of the sum. Application is made to stationary solutions of the first order random difference equation in and to the pth order random difference equation Under circumstances where explicit solution of the difference equations is impossible, this provides some information about the form of the solution.
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