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Theory of Stochastic Processes, 2010, Volume 16(32), Issue 1, Pages 29–38 (Mi thsp57)  
On the convergence of series of autoregressive sequences in Banach spaces

Valerii V. Buldygin, Marina K. Runovska

Department of Math. Anal. and Probab. Theory, National Technical University of Ukraine (KPI), Peremogy Ave., 37, Kyiv 03056, Ukraine
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Abstract: Necessary and sufficient conditions for the almost sure convergence of a series of autoregressive sequences in separable Banach spaces are studied. As an application of the obtained results, the condition for the admissible shift of a zero-mean Gaussian Markov measure is considered.
Keywords: Autoregressive sequences, almost sure convergence of random series, summability theory, Gaussian Markov sequences, continuity and singularity of probabilistic measures.
Bibliographic databases:
Document Type: Article
MSC: Primary 60G50, 60G15; Secondary 40C05, 60G30
Language: English
Citation: Valerii V. Buldygin, Marina K. Runovska, “On the convergence of series of autoregressive sequences in Banach spaces”, Theory Stoch. Process., 16(32):1 (2010), 29–38
Citation in format AMSBIB
\Bibitem{BulRun10}
\by Valerii V. Buldygin, Marina K. Runovska
\paper On the convergence of series of autoregressive sequences in Banach spaces
\jour Theory Stoch. Process.
\yr 2010
\vol 16(32)
\issue 1
\pages 29--38
\mathnet{http://mi.mathnet.ru/thsp57}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2779843}
\zmath{https://zbmath.org/?q=an:1224.60094}
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