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, 38:4, 694–705

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