The estimation of accuracy of simulation of sub-Gaussian random processes
Let a random process \(X(t)\), \(t\in T\), have the representation \(X(t)=\sum_{k=1}^{\infty}f_{k}(t)\xi_{k}\), where \(\{\xi_{k}\}\) is a family of strong sub-Gaussian random variables. The process \(X_{M}(t)=\sum_{k=1}^{M}f_{k}(t)\xi_{k}\), \(t\in T,\) is called model of the process \(X(t)\). Let us suppose that processes \(X(t), X_{M}(t)\in C(T), M=1,2,\ldots\), where \(C(T)\) is the space of continuous bounded functions with norm \(\|x(t)\|_{C}=\sup_{t\in T}|x(t)|\). The author obtains estimates of accuracy of simulation by \(X_{M}(t)\) of the process \(X(t)\) in the cases of Karhunen-Loeve decomposition, the Fourier decomposition and stationary process with discrete spectrum.
scientific article; zbMATH DE number 1698083