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Moving averages with random coefficients and random coefficient autoregressive models. (English) Zbl 0747.60062

From the authors’ abstract: Let \(\sigma=\sum_ n C_ n Z_ n\), where the \(\{Z_ n\}\) are independent and identically distributed \(d\)- dimensional random vectors taking on nonnegative values and the \(\{C_ n\}\) are random matrices independent of \(\{Z_ n\}\). If the distribution of \(Z_ 1\) is multivariate regularly varying at infinity, then under suitable summability conditions on the \(\{C_ n\}\), so is the sum \(\sigma\). Application is made to stationary solutions of the first order \(d\)-dimensional random difference equation \(X_{n+1}=M_{n+1}X_ n+Q_{n+1}\). The \(\{Q_ n\}\) are assumed to be i.i.d. \(d\)-dimensional random vectors independent of the i.i.d. random square matrices \(\{M_ i\}\).

MSC:

60H99 Stochastic analysis
60E99 Distribution theory
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