Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

References

[1] S. R. Asmussen and P. W. Glynn, Stochastic Simulation: Algorithms and Analysis, Stoch. Model. Appl. Probab. 57, Springer, New York, 2007. 10.1007/978-0-387-69033-9Search in Google Scholar

[2] A. Ayache and M. S. Taqqu, Rate optimality of wavelet series approximations of fractional Brownian motion, J. Fourier Anal. Appl. 9 (2003), no. 5, 451–471. 10.1007/s00041-003-0022-0Search in Google Scholar

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

[4] S. Cambanis and E. Masry, Wavelet approximation of deterministic and random signals: Convergence properties and rates, IEEE Trans. Inform. Theory 40 (1994), no. 4, 1013–1029. 10.1109/18.335971Search in Google Scholar

[5] G. Didier and V. Pipiras, Gaussian stationary processes: adaptive wavelet decompositions, discrete approximations, and their convergence, J. Fourier Anal. Appl. 14 (2008), no. 2, 203–234. 10.1007/s00041-008-9012-6Search in Google Scholar

[6] B. V. Dovgay, Y. V. Kozachenko and I. V. Rozora, Simulation of Random Processes in Physical Systems (in Ukrainian), Zadruga, Kyiv, 2010. Search in Google Scholar

[7] W. Härdle, G. Kerkyacharian, D. Picard and A. Tsybakov, Wavelets, Approximation, and Statistical Applications, Lect. Notes Stat. 129, Springer, New York, 1998. 10.1007/978-1-4612-2222-4Search in Google Scholar

[8] E. Hernández and G. Weiss, A First Course on Wavelets, Stud. Adv. Math., CRC Press, Boca Raton, 1996. 10.1201/9780367802349Search in Google Scholar

[9] Y. Kozachenko, A. Olenko and O. Polosmak, Uniform convergence of wavelet expansions of Gaussian random processes, Stoch. Anal. Appl. 29 (2011), no. 2, 169–184. 10.1080/07362994.2011.532034Search in Google Scholar

[10] Y. Kozachenko, A. Olenko and O. Polosmak, Uniform convergence of compactly supported wavelet expansions of Gaussian random processes, Comm. Statist. Theory Methods 43 (2014), no. 10–12, 2549–2562. 10.1080/03610926.2013.784338Search in Google Scholar

[11] Y. Kozachenko and O. Pogoriliak, Simulation of Cox processes driven by random Gaussian field, Methodol. Comput. Appl. Probab. 13 (2011), no. 3, 511–521. 10.1007/s11009-010-9169-8Search in Google Scholar

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

[13] Y. Kozachenko, T. Sottinen and O. Vasylyk, Simulation of weakly self-similar stationary increment Subφ⁢(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] Y. Kozachenko and Y. Turchyn, On Karhunen–Loeve-like expansion for a class of random processes, Int. J. Stat. Manag. Syst. 3 (2008), 43–55. Search in Google Scholar

[15] 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

[16] 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

[17] 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

[18] O. Kurbanmuradov and K. Sabelfeld, Convergence of Fourier-wavelet models for Gaussian random processes, SIAM J. Numer. Anal. 46 (2008), no. 6, 3084–3112. 10.1137/070699408Search in Google Scholar

[19] O. Kurbanmuradov, K. Sabelfeld and P. R. Kramer, Randomized spectral and Fourier-wavelet methods for multidimensional Gaussian random vector fields, J. Comput. Phys. 245 (2013), 218–234. 10.1016/j.jcp.2013.03.021Search in Google Scholar

[20] E. Masry, Convergence properties of wavelet series expansions of fractional Brownian motion, Appl. Comput. Harmon. Anal. 3 (1996), no. 3, 239–253. 10.1006/acha.1996.0019Search in Google Scholar

[21] Y. Meyer, F. Sellan and M. S. Taqqu, Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion, J. Fourier Anal. Appl. 5 (1999), no. 5, 465–494. 10.1007/BF01261639Search in Google Scholar

[22] V. Pipiras, Wavelet-type expansion of the Rosenblatt process, J. Fourier Anal. Appl. 10 (2004), no. 6, 599–634. 10.1007/s00041-004-3004-ySearch in Google Scholar

[23] V. Pipiras, Wavelet-based simulation of fractional Brownian motion revisited, Appl. Comput. Harmon. Anal. 19 (2005), no. 1, 49–60. 10.1016/j.acha.2005.01.002Search in Google Scholar

[24] O. Rivasplata, Subgaussian random variables: An expository note, Technical Report, University of Alberta, Alberta, 2012. Search in Google Scholar

[25] M. A. Stoksik, R. G. Lane and D. T. Nguyen, Accurate synthesis of fractional Brownian motion using wavelets, Electron. Lett. 30 (1994), 383–384. 10.1049/el:19940269Search in Google Scholar

[26] I. Turchyn, A multiplicative wavelet-based model for simulation of a random process, Mod. Stoch. Theory Appl. 2 (2015), no. 4, 309–325. 10.15559/15-VMSTA33Search in Google Scholar

[27] Y. V. Turchyn, Simulation of sub-Gaussian processes using wavelets, Monte Carlo Methods Appl. 17 (2011), no. 3, 215–231. 10.1515/mcma.2011.010Search in Google Scholar

[28] G. Walter and J. Zhang, A wavelet-based KL-like expansion for wide-sense stationary random processes, IEEE Trans. Signal Process. 42 (1994), 1737–1745. 10.1109/78.298281Search in Google Scholar

[29] P. Zhao, G. Liu and C. Zhao, A matrix-valued wavelet KL-like expansion for wide-sense stationary random processes, IEEE Trans. Signal Process. 52 (2004), no. 4, 914–920. 10.1109/TSP.2004.823499Search in Google Scholar