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

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  • Turchyn Ievgen

    (Mechanics and Mathematics Department, Oles Honchar Dnipro National University, 72, Gagarin Av., Dnipro, 49010, Ukraine)

Abstract

We consider stochastic processes Y⁢(t){Y(t)} which can be represented as Y⁢(t)=(X⁢(t))s{Y(t)=(X(t))^{s}}, s∈ℕ{s\in\mathbb{N}}, where X⁢(t){X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates Y⁢(t){Y(t)} with given accuracy and reliability in Lp⁢([0,T]){L_{p}([0,T])}. A model for simulation with given accuracy and reliability in Lp⁢([0,T]){L_{p}([0,T])} is also built for processes Z⁢(t){Z(t)} which can be represented as Z⁢(t)=X1⁢(t)⁢X2⁢(t){Z(t)=X_{1}(t)X_{2}(t)}, where X1⁢(t){X_{1}(t)} and X2⁢(t){X_{2}(t)} are independent stationary strictly sub-Gaussian processes.

Suggested Citation

  • Turchyn Ievgen, 2019. "Wavelet-based simulation of random processes from certain classes with given accuracy and reliability," Monte Carlo Methods and Applications, De Gruyter, vol. 25(3), pages 217-225, September.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:3:p:217-225:n:3
    DOI: 10.1515/mcma-2019-2042
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    References listed on IDEAS

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    1. Kurbanmuradov O. & Sabelfeld K., 2006. "Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 395-445, November.
    2. Yuriy Kozachenko & Andriy Olenko & Olga Polosmak, 2014. "Uniform Convergence of Compactly Supported Wavelet Expansions of Gaussian Random Processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2549-2562, May.
    3. Yurij Kozachenko & Oleksandr Pogoriliak, 2011. "Simulation of Cox Processes Driven by Random Gaussian Field," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 511-521, September.
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    More about this item

    Keywords

    Wavelets; sub-Gaussian random processes; simulation; 60G10; 42C40;
    All these keywords.

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