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Stochastic Spectral and Fourier-Wavelet Methods for Vector Gaussian Random Fields

Author

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  • Kurbanmuradov O.

    (1. Center for Phys. Math. Research, Turkmenian State University, Turkmenbashy av. 31, 744000 Ashgabad, Turkmenistan)

  • Sabelfeld K.

    (2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D – 10117 Berlin, Germany sabelfel@wias-berlin.de)

Abstract

Randomized Spectral Models (RSM) and Randomized Fourier-Wavelet Models (FWM) for simulation of homogeneous Gaussian random fields based on spectral representations and plane wave decomposition of random fields are developed. Extensions of FWM to vector random processes are constructed. Convergence of the constructed Fourier-Wavelet models (in the sense of finite-dimensional distributions) under some general conditions on the spectral tensor is given. A comparative analysis of RSM and FWM is made by calculating Eulerian statistical characteristics of a 3D isotropic incompressible random field through an ensemble and space averaging.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:5:p:395-445:n:8
    DOI: 10.1515/156939606779329080
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    References listed on IDEAS

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    1. Kurbanmuradov O. & Sabelfeld K. & Smidts O.F. & Vereecken H., 2003. "A Lagrangian Stochastic Model for the Transport in Statistically Homogeneous Porous Media," Monte Carlo Methods and Applications, De Gruyter, vol. 9(4), pages 341-366, December.
    2. Kurbanmuradov O. & Sabelfeld K. & Koluhin D., 1997. "Stochastic Lagrangian Models for Two-Particle Motion in Turbulent Flows. Numerical Results," Monte Carlo Methods and Applications, De Gruyter, vol. 3(3), pages 199-224, December.
    3. Kramer Peter R., 2001. "A Review of Some Monte Carlo Simulation Methods for Turbulent Systems," Monte Carlo Methods and Applications, De Gruyter, vol. 7(3-4), pages 229-244, December.
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    Cited by:

    1. 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.
    2. Sabelfeld Karl, 2008. "Expansion of random boundary excitations for elliptic PDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 13(5-6), pages 405-453, January.
    3. Sabelfeld K. & Kurbanmuradov O. & Levykin A., 2009. "Stochastic simulation of particle transport by a random Darcy flow through a porous cylinder," Monte Carlo Methods and Applications, De Gruyter, vol. 15(1), pages 63-90, January.

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