Estimation of Accuracy and Reliability of Models of φ-sub-Gaussian Stochastic Processes in Spaces

Oleksandr M. Mokliachuk

Abstract


Background. At present, in the theory of stochastic process modeling a problem of assessment of reliability and accuracy of stochastic process model in C(T) space wasn’t studied for the case of inexplicit decomposition of process in the form of a series with independent terms.

Objective. The goal is to study reliability and accuracy in C(T) of models of processes from Subφ(Ω) that cannot be decomposed in a series with independent elements explicitly.

Methods. Using previous research in the field of modeling of stochastic processes, assumption is considered about possibility of decomposition of a stochastic process in the series with independent elements that can be found using approximations.

Results. Impact of approximation error of process decomposition in series with independent elements on reliability and accuracy of modeling of stochastic process in C(T) is studied.

Conclusions. Theorems are proved that allow estimation of reliability and accuracy of a model in C(T) of a stochastic process from Subφ(Ω) in the case when decomposition of this process in a series with independent elements can be found only with some error, for example, using numerical approximations.


Keywords


Stochastic processes; φ-sub-Gaussian processes; Models of stochastic processes; Reliability and accuracy of models of stochastic processes

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References


O.I. Vasylyk et al., φ-Sub-Gaussian Stochastic Processes. Kyiv, Ukraine: Kyiv University, 2008.

Yu.V. Kozachenko and I.V. Rozora, “Accuracy and reliability of models of stochastic processes of the space Subφ(Ω)”, Theor. Probab. Math. Statist., no. 71, pp. 105–117, 2005.

Yu. Kozachenko and N.V. Troshki, “Accuracy and reliability of a model of Gaussian random processes in C(T) space”, Int. J. Stat. Manag. Syst., vol. 10, no. 1-2, pp. 1–15, 2015.

Yu.V. Kozachenko and A.O. Pashko, Modeling of Stochastic Processes. Kyiv, Ukraine: Kyiv University, 1999.

O.M. Mokliachuk, “Simulation of random processes with known correlation function with the help of Karhunen–Loeve decomposition”, Theory of Stochastic Processes, iss. 13 (29), no. 4, pp. 90–94, 2007.

Yu.V. Kozachenko and O.M. Moklyachuk, “Sample continuity and modeling of stochastic processes from the spaces DV,W”, Theor. Probab. Math. Statist., no 83, pp. 95–110, 2011.

O.M. Moklyachuk, “Models with given reliability and accuracy in Lp(T) of stochastic processes from Subφ(Ω) that can be represented in series with independent elements”, Prykladna Statystyka. Aktuarna ta Finansova Matematyka, no. 2, pp. 24–29, 2012 (in Ukrainian).

O. Mokliachuk, “Modeling of stochastic processes in Lp(T) using orthogonal polynomials”, Universal J. Appl. Math., vol. 2, pp. 141–147, 2014. doi: 10.13189/ujam.2014.020304

V.V. Buldygin and Yu.V. Kozachenko, Metric Characterization of Random Variables and Random Processes (Trans. Math. Monographs, vol. 188). Providence,RI: AMS, American Mathematical Society, XII, 2000.

Yu.V. Kozachenko and E.I. Ostrovskij, “Banach spaces of random variables of sub-Gaussian type”, Theor. Probab. Math. Statist., no. 32, pp. 45–56, 1986.


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DOI: https://doi.org/10.20535/1810-0546.2017.4.105428

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