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On one way of modeling a stochastic process with given accuracy and reliability

  • Tetiana Ianevych ORCID logo EMAIL logo , Iryna Rozora ORCID logo and Anatolii Pashko ORCID logo

Abstract

The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ( [ 0 , T ] ) .

Acknowledgements

We are grateful to the anonymous referee for the insightful comments that have significantly improved the paper.

References

[1] O. M. Belotserkovskiĭ and Y. I. Khlopkov, Monte Carlo methods in applied mathematics and computational aerodynamics, Comput. Math. Math. Phys. 46 (2006), 1418–1441. 10.1134/S0965542506080124Search in Google Scholar

[2] 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

[3] Y. V. Kozachenko and A. O. Pashko, On the modeling of random fields. I, Theory Probab. Math. Stat. 61 (2000), 61–74. Search in Google Scholar

[4] Y. V. Kozachenko and A. O. Pashko, On the modeling of random fields. II, Theory Probab. Math. Stat. 62 (2001), 51–63. Search in Google Scholar

[5] Y. Kozachenko, A. O. Pashko and I. V. Rozora, Simulation of Random Processes and Fields (in Ukrainian), “Zadruga”, Kyiv, 2007. Search in Google Scholar

[6] Y. V. Kozachenko and M. Petranova, Simulation of Gaussian stationary Ornstein–Uhlenbeck process with given reliability and accuracy in space C ( [ 0 , T ] ) , Monte Carlo Methods Appl. 23 (2017), no. 4, 277–286. 10.1515/mcma-2017-0115Search in Google Scholar

[7] Y. V. Kozachenko, O. O. Pogorilyak, I. Rozora and A. M. Tegza, Simulation of Stochastic Processes with Given Accuracy and Reliability, Elsevier, Amsterdam, 2016. 10.1016/B978-1-78548-217-5.50006-4Search in Google Scholar

[8] Y. V. Kozachenko and I. V. Rozora, Simulation of Gaussian stochastic processes, Random Oper. Stoch. Equ. 11 (2003), no. 3, 275–296. 10.1163/156939703771378626Search in Google Scholar

[9] Y. V. Kozachenko and I. V. Rozora, Accuracy and reliability of modeling random processes in the space S u b ϕ ( Ω ) , Theory Probab. Math. Stat. 71 (2005), 105–117. 10.1090/S0094-9000-05-00651-4Search in Google Scholar

[10] Y. V. Kozachenko and I. V. Rozora, Construction of a Karhunen–Loeve model for the input of a Gaussian process applied to a linear system taking output into account, Theory Probab. Math. Stat. 99 (2019), 101–112. Search in Google Scholar

[11] 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

[12] Y. V. Kozachenko, I. V. Rozora and Y. V. Turchyn, Properties of some random series, Comm. Statist. Theory Methods 40 (2011), no. 19–20, 3672–3683. 10.1080/03610926.2011.581188Search in Google Scholar

[13] Y. V. Kozachenko, T. Sottinen and O. Vasylyk, Simulation of weakly self-similar stationary increment S u b ϕ ( Ω ) -processes: A series expansion approach, Methodol. Comput. Appl. Probab. 7 (2005), no. 3, 379–400. 10.1007/s11009-005-4523-ySearch in Google Scholar

[14] 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

[15] A. O. Pashko, O. V. Lukovych, I. V. Rozora, T. A. Oleshko and O. I. Vasylyk, Analysis of simulation methods for fractional Brownian motion in the problems of intelligent systems design, IEEE International Conference on Advanced Trends in Information Theory—ATIT 2019, IEEE Press, Piscataway (2019), 373–378. 10.1109/ATIT49449.2019.9030478Search in Google Scholar

[16] A. O. Pashko and I. V. Rozora, Accuracy of simulation for the network traffic in the form of fractional Brownian motion, 14th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering—TCSET 2018, IEEE Press, Piscataway (2018), 840–845. 10.1109/TCSET.2018.8336328Search in Google Scholar

[17] S. Prigarin, Models of Random Processes and Fields in Monte Carlo Methods, Palmarium Academic, Chisinau, 2014. Search in Google Scholar

[18] S. Prigarin, K. Hahn and G. Winkler, Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion, Siberian J. Numer. Math. 11 (2008), no. 2, 201–218. 10.1134/S1995423908020079Search in Google Scholar

[19] I. Rozora and M. Lyzhechko, On the modeling of linear system input stochastic processes with given accuracy and reliability, Monte Carlo Methods Appl. 24 (2018), no. 2, 129–137. 10.1515/mcma-2018-0011Search in Google Scholar

[20] K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems, Springer Ser. Comput. Math., Springer, Berlin, 1991. 10.1007/978-3-642-75977-2Search in Google Scholar

[21] K. K. Sabelfeld and N. A. Simonov, Random Walks on Boundary for Solving PDEs, VSP, Utrecht, 1994. 10.1515/9783110942026Search in Google Scholar

[22] A. M. Yaglom, Correlation theory of stationary and related random functions. Vol. II, Springer Ser. Statist., Springer, New York, 1987. 10.1007/978-1-4612-4620-6Search in Google Scholar

[23] S. Yermakov, S. Jacobson and J. Ramsey, Computer simulations of electrokinetic transport in microfabricated channel structures, Anal Chem. 70 (1998), no. 21, 4494–4504. 10.1021/ac980551wSearch in Google Scholar PubMed

[24] S. Yermakov and G. Mikhailov, Statistical Simulation (in Russian), “Nauka”, Moscow, 1982. Search in Google Scholar

Received: 2021-07-23
Revised: 2022-01-24
Accepted: 2022-02-05
Published Online: 2022-03-26
Published in Print: 2022-06-01

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