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- W2123006142 abstract "A $d$-dimensional $mathrm{RCA}(1)$ process is a generalization of the $d$-dimensional $mathrm{AR}(1)$ process, such that the coefficients ${M_{t};t=1,2,ldots}$ are i.i.d. random matrices. In the case $d=1$, under a nondegeneracy condition, Goldie and Maller gave necessary and sufficient conditions for the convergence in distribution of an $mathrm{RCA}(1)$ process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition $Vert{prod_{t=1}^{n}M_{t}}Vertstackrel{mathrm{a.s.}}{longrightarrow}0$ as $ntoinfty$, most of the results of Goldie and Maller can be extended to the case $d>1$. If this condition does not hold, some of their results cannot be extended." @default.
- W2123006142 created "2016-06-24" @default.
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- W2123006142 date "2014-05-01" @default.
- W2123006142 modified "2023-09-29" @default.
- W2123006142 title "Conditions for convergence of random coefficient $mathrm{AR}(1)$ processes and perpetuities in higher dimensions" @default.
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- W2123006142 doi "https://doi.org/10.3150/13-bej513" @default.
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