Pre-Gaussian processes and convergence in \(C(T)\) of estimators of covariance functions. (English. Russian original) Zbl 0834.60038

Kozachenko, Yu. V.; Stadnik, A. I.

Theory Probab. Math. Stat. 45, 51-57 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 54-62 (1991).

Summary: Estimates are obtained for \(P \{\sup_{t \in T} |\eta (t) |> x\}\) in the case of a pre-Gaussian random process \(\eta (t)\). These results are applied to the investigation of conditions for convergence and of the rate of convergence in \(C(T)\) of estimators of the covariance function of a stationary Gaussian random process.

MSC:

60G15	Gaussian processes
60G10	Stationary stochastic processes
41A25	Rate of convergence, degree of approximation
62G05	Nonparametric estimation
62G15	Nonparametric tolerance and confidence regions

Keywords:

conditions for convergence; rate of convergence; stationary Gaussian random process