Resnick, Sidney I.; Willekens, Eric Moving averages with random coefficients and random coefficient autoregressive models. (English) Zbl 0747.60062 Commun. Stat., Stochastic Models 7, No. 4, 511-525 (1991). 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 \(\{M_ i\}\). Reviewer: K.S.Miller (Rye Brook) Cited in 1 ReviewCited in 49 Documents MSC: 60H99 Stochastic analysis 60E99 Distribution theory Keywords:difference equations; stationary solutions PDFBibTeX XMLCite \textit{S. I. Resnick} and \textit{E. Willekens}, Commun. Stat., Stochastic Models 7, No. 4, 511--525 (1991; Zbl 0747.60062) Full Text: DOI