Almost Sure Convergence of the Series of Gaussian Markov Sequences

DOI10.1080/03610926.2011.581163zbMath1315.60047OpenAlexW2084794046MaRDI QIDQ2890076

V. V. Buldygin, Marina K. Runovska

Publication date: 8 June 2012

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610926.2011.581163

zbMATH Keywords

Gaussian Markov sequencealmost sure convergence of random seriesGaussian \(m\)-Markov sequencemulti-dimensional Gaussian Markov sequenceoperator-normed sums of independent random vectors

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Convergence and divergence of series and sequences (40A05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (3)

A refinement of conditions for the almost sure convergence of series of multidimensional regression sequences ⋮ On the convergence of the Baum-Katz series for elements of a linear autoregression ⋮ Complete moment convergence for randomly weighted sums of arrays of rowwise \(m_n\)-extended negatively dependent random variables and its applications

Cites Work

• Asymptotic behavior of solutions of stochastic recurrence equations in \(\mathbb{R}{}^ d\)
• The Strong Law of Large Numbers for Sums of Independent Random Vectors with Operator Normalizations and Null Convergence of Gaussian Sequences
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