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Teoriya Veroyatnostei i ee Primeneniya, 1993, Volume 38, Issue 4, Pages 827–841 (Mi tvp4020)  

On sample continuity of multidimensional Gaussian Markov processes

S. A. Solntsev

Kiev Polytechnic Institute
Abstract: The main result of the paper is Theorem 4. It gives necessary and sufficient entropy conditions for sample continuity of a multidimensional Gaussian Markov process. The method of proof is based on the results of [3], where the problem of sample continuity of trajectories of a Gaussian process was reduced to the problem of almost sure convergence of specially constructed Gaussian sequences.
Keywords: $\varepsilon$-entropy, Sudakov entropy conditions, sample continuity of Gaussian processes, almost sure convergence of Gaussian sequences.
Received: 13.01.1989
English version:
Theory of Probability and its Applications, 1993, Volume 38, Issue 4, Pages 694–705
DOI: https://doi.org/10.1137/1138068
Bibliographic databases:
Language: Russian
Citation: S. A. Solntsev, “On sample continuity of multidimensional Gaussian Markov processes”, Teor. Veroyatnost. i Primenen., 38:4 (1993), 827–841; Theory Probab. Appl., 38:4 (1993), 694–705
Citation in format AMSBIB
\Bibitem{Sol93}
\by S.~A.~Solntsev
\paper On sample continuity of multidimensional Gaussian Markov processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1993
\vol 38
\issue 4
\pages 827--841
\mathnet{http://mi.mathnet.ru/tvp4020}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1318000}
\zmath{https://zbmath.org/?q=an:0829.60030}
\transl
\jour Theory Probab. Appl.
\yr 1993
\vol 38
\issue 4
\pages 694--705
\crossref{https://doi.org/10.1137/1138068}
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