Linear approximation of random processes and sampling design problems (Q2769708)

Spline approximation of a random process based on \(n\) observations and derivatives of the process is considered. The Hermite spline interpolation of locally stationary processes and the best approximation order for Hölder's classes of random processes are studied in detail. The quality of the approximation is measured by integrated or maximal quadratic mean error. The sequence of designs for Hermite interpolation splines with asymptotically optimal properties is found. The proposed approach can also be applied to numerical integration and differentiation.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].