Mikhajlov, A. E. On oscillation of Gaussian processes. (Russian) Zbl 0711.60034 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 177, 92-97 (1989). [For the entire collection see Zbl 0698.00031.] Let (\(\Omega\),F,P) be a probability space, X a separable Banach space and \({\mathcal C}\) a Gaussian process on (\(\Omega\),F,P) with values in X. The author proves for all \(c_ 0\in {\mathcal C}\) the existence of a set \(K^{{\mathcal C}}_{c_ 0}\) such that the oscillation of the process \({\mathcal C}\) at the point \(c_ 0\) is almost surely equal to \(K^{{\mathcal C}}_{c_ 0}\). The results obtained are then used for the study of the behavior of a one-dimensional Gaussian process in the neighborhoods of the points in which the Ito-Nisio oscillation differs from zero. Reviewer: D.Aissani Cited in 3 Reviews MSC: 60G15 Gaussian processes Keywords:Gaussian process; oscillation; Ito-Nisio oscillation Citations:Zbl 0698.00031 PDFBibTeX XML Full Text: EuDML