Simulation accuracy of stationary Gaussian stochastic processes inL ²(0,T)

Abstract

Models of stationary Gaussian stochastic processes with discrete and continuous spectra are constructed. Simulation of stationary Gaussian processes with a continuous spectrum is considered for the following cases: when the covariance function of the stochastic process is expandable in a Fourier series with positive coefficients; when the spectrum of the stationary Gaussian stochastic process is concentrated on the interval [0, Λ]; and in the general case. The stationary Gaussian process is simulated with prescribed reliability and accuracy in L²(0, T).