On the modelling of Gaussian stationary processes with absolutely continuous spectrum. (English. Russian original) Zbl 0839.60041

Kozachenko, Yu. V.; Kozachenko, L. F.

Theory Probab. Math. Stat. 47, 49-55 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 47-54 (1992).

The problem of the Gaussian stationary random process simulation is treated. The process is described by given continuous covariance function having a local maximum at the zero argument, and continuous spectrum. To simulate the process the sum of \(N\) binomial harmonic terms is used. Each term is the superposition of sine and cosine functions with statistically independent weights having similar variances. Frequencies of harmonics are equidistantly distributed within some band \([0; L]\). The criterion used for the simulation is as follows. The permissible mean square on the considered time interval \([0;T]\) discrepancy \(E\) between the initial and simulated processes, and the maximal permissible probability \(P(E)\) of this discrepancy are to be chosen. Starting from the values \(E\) and \(P\), the number \(N\) and band \(L\) are determined. Thus, the problem is solved.

Reviewer: A.V.Yakimov (Novgorod)

MSC:

60G15	Gaussian processes
60G10	Stationary stochastic processes
42A10	Trigonometric approximation

Keywords:

Gaussian stationary process; modelling; spectrum