Moving averages with random coefficients and random coefficient autoregressive models

Consider the series ¿n CnZn where Zn are iid -valued random vectors and Cn are random matrices independent of the Zn. Under suitable summability conditions on the Cn, if the distribution of Z1 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