Theory of Probability and Mathematical Statistics
A refinement of conditions for the almost sure convergence of series of multidimensional regression sequences
M. K. Ilienko
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Abstract: We obtain a general criterion for the almost sure convergence of a series whose terms are elements of a multidimensional autoregressive sequence with arbitrary matrix coefficients. In particular, the case of degenerate matrices is also considered. This result extends an earlier result by Buldygin and Runovska who obtained necessary and sufficient conditions for the almost sure convergence of a random series whose terms are elements of a multidimensional Gaussian Markov sequence with nondegenerate matrix coefficients.
Keywords: Multidimensional regression sequences, m-regression sequences of random variables, almost sure convergence of random series
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