Simulation of a Gaussian stationary process with a stable correlation function with a given reliability and accuracy

Petranova, M. Y. (2020). Simulation of a Gaussian stationary process with a stable correlation function with a given reliability and accuracy. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 89–95. https://doi.org/10.17721/1812-5409.2020/3.9

In this paper, the representation of random processes in the form of random series with uncorrelated members obtained in the work by Yu. V. Kozachenko, I.V. Rozora, E.V. Turchina (2007) [1]. Similar constructions were studied in the book by Yu. V. Kozachenko and others. [2] in the general case. However, there are additional difficulties in construction of models of specific process, such as, for example, selection of the appropriate basis in L_2(R). In this paper, models are constructed that approximate the Gaussian process with a stable correlation function $\rho_{\alpha} (h) = E X_{\alpha}(t + h) X_{\alpha}(t) = B^2 \exp{-d|h|^{\alpha}}, \alpha > 0, d > 0$ with parameter $\alpha = 2$, which is a centered stationary process with a given reliability and accuracy in the space L_p ([0,T]). And also the rates of convergence of the models are found, the corresponding theorems are formulated. Methods of representation and main properties of the process with a stable correlation function $\rho_2(h) = B^2 \exp{-d|h|^2}, d > 0$ are considered. As a basis in the space L_2(T) Hermitian functions are used.Key words: correlation function, simulation, model of the process, accuracy, reliability.Pages of the article in the issue: 89 - 95Language of the article: Ukrainian