Simulation of a Gaussian stationary process with a stable correlation function with a given reliability and accuracy
DOI:
https://doi.org/10.17721/1812-5409.2020/3.9Abstract
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 - 95
Language of the article: Ukrainian
References
KOZACHENKO, YU.V., ROZORA, I.V., TURCHYN, YE. V. (2007) On expansion of random process in series. Random Operators and Stohastic Equations. v. 15(1). P. 15–35.
KOZACHENKO, YU.V., MLAVETS, YU. YU., MOKLIACHUK, O.M. (2015) Kvazibanakhovi prostory vypadkovykh velychyn. Uzhhorod: Karpaty.
UHLENBECK, G.E., ORNSTEIN, L.S. (1930) On the theory of Brownian motion Phys. Rev. v. 36 P. 832–841.
KAMPE DE FERIET J. (1957) Fonctions de la Physique Mathematique. Paris: Paris Editions du CNRS.
ERDELYI, A. (1953) Higher Transcendental Functions. New-York: McGraw-Hill. Vol. II.
KAMENSCHIKOVA, O., KOZACHENKO, Y. (2009) On an expansion of random processes in the space L_p(T). Theory Probab. And Math. Statist.. v.79. P. 83–88.
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