×

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

MSC:

60G15 Gaussian processes

Citations:

Zbl 0698.00031
Full Text: EuDML