×

On approximation of some stochastic processes by splines. (Russian) Zbl 0601.41018

The stochastic processes x(t) with a derivative which is continuous on [0,1] in the mean quadratic sense are considered. The mean quadratic estimation of the approximation \(M(x(t)-x_ n(t))^ 2\) and the approximation of the process derivative Dx(t) \(M| Dx(t)-Dx_ n(t)|^ 2,\) where \(x_ n(t)\) is a truncated Fourier expansion of x(t), in terms of the orthogonal spline system are given. These estimates are easy to use in the approximative calculus of integrals.
Reviewer: C.Simerska

MSC:

41A15 Spline approximation
60G99 Stochastic processes
PDFBibTeX XMLCite
Full Text: EuDML