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Simulation of Gaussian stationary Ornstein–Uhlenbeck process with given reliability and accuracy in space C([0,T])

  • Yuriy Kozachenko EMAIL logo and Marina Petranova

Abstract

In this paper, we construct models that approximate the Gaussian stationary Ornstein–Uhlenbeck process with given reliability 1-δ, 0<δ<1, and accuracy β>0 in the space C([0,T]).

MSC 2010: 60G10; 60G15

References

[1] V. V. Buldygin and Y. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, Transl. Math. Monogr. 188, American Mathematical Society, Providence, 2000. 10.1090/mmono/188Search in Google Scholar

[2] Y. V. Kozachenko and A. O. Pashko, The accuracy and reliability of random processes and fields simulation in uniform metrics (in Ukrainian), Sik Group Ukraine, Kiev, 2016. Search in Google Scholar

[3] Y. V. Kozachenko, A. O. Pashko and I. V. Rozora, Simulation Random Processes and Fields (in Ukrainian), Kiyv, 2007. Search in Google Scholar

[4] Y. Kozachenko, O. Pogorilyak, I. Rozora and A. Tegza, Simulation of Stochastic Processes with Given Accuracy and Reliability, Math. Statist. Ser., ISTE, London, 2016. 10.1016/B978-1-78548-217-5.50006-4Search in Google Scholar

[5] Y. Kozachenko, O. Pogorilyak and A. Tegza, Simulation Gaussian Random Processes and Cox Processes (in Ukrainian), Uzhhorod, Karpaty, 2012. Search in Google Scholar

[6] Y. V. Kozachenko and I. V. Rozora, A criterion for testing hypothesis about impulse response function, Stat. Optim. Inf. Comput. 4 (2016), no. 3, 214–232. 10.19139/soic.v4i3.222Search in Google Scholar

[7] Y. V. Kozachenko, I. V. Rozora and Y. V. Turchyn, On an expansion of random processes in series, Random Oper. Stoch. Equ. 15 (2007), no. 1, 15–33. 10.1515/ROSE.2007.002Search in Google Scholar

[8] P. R. Kramer, O. Kurbanmuradov and K. Sabelfeld, Comparative analysis of multiscale Gaussian random field simulation algorithms, J. Comput. Phys. 226 (2007), no. 1, 897–924. 10.1016/j.jcp.2007.05.002Search in Google Scholar

[9] O. Kurbanmuradov and K. Sabelfeld, Stochastic spectral and Fourier–Wavelet methods for vector Gaussian random fields, Monte Carlo Methods Appl. 12 (2006), no. 5–6, 395–445. 10.1515/156939606779329080Search in Google Scholar

[10] E. Lukacs, Characteristic functions, 2nd. ed., Hafner Publishing, New York, 1970. Search in Google Scholar

[11] V. A. Ogorodnikov and S. M. Prigarin, Numerical Modelling of Random Processes and Fields, VSP, Utrecht, 1996. 10.1515/9783110941999Search in Google Scholar

[12] M. Petranova, Simulation of Gaussian stationary quasi Ornstein–Uhlenbeck process with given reliability and accuracy in spaces C([0,T]) and Lp([0,T]), J. Appl. Math. Stat. 3 (2016), no. 1, 44–58. 10.7726/jams.2016.1004Search in Google Scholar

Received: 2017-7-17
Accepted: 2017-10-4
Published Online: 2017-11-14
Published in Print: 2017-12-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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