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Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies

Author

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  • Grigoriu Mircea

    (School of Civil & Environmental Engineering, Cornell University, Ithaca,NY 14853-3501, USA)

Abstract

An algorithm is developed for generating samples of vector-valued Gaussian processes and fields. The algorithm is based on Karhunen–Loève (KL) representations of vector-valued random functions Z⁢(x){Z(x)} with finite variances and their construction involves two steps. First, truncation levels {mi}{\{m_{i}\}} are selected for the KL representations of the components {Zi⁢(x)}{\{Z_{i}(x)\}} of Z⁢(x){Z(x)} such that they meet imposed accuracies. Second, the truncation levels {mi}{\{m_{i}\}} are accepted or increased if the accuracies of resulting cross correlation functions of Z⁢(x){Z(x)} satisfy or violate preset constraints. Theoretical arguments are used to prove the validity of the proposed KL-based models of Z⁢(x){Z(x)}. The models are applied to develop an efficient Monte Carlo algorithm for generating samples of vector-valued Gaussian functions. Numerical examples illustrate the implementation of the proposed Monte Carlo algorithm and demonstrate its performance.

Suggested Citation

  • Grigoriu Mircea, 2017. "Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies," Monte Carlo Methods and Applications, De Gruyter, vol. 23(3), pages 165-188, September.
    • Handle: RePEc:bpj:mcmeap:v:23:y:2017:i:3:p:165-188:n:3
    DOI: 10.1515/mcma-2017-0112
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    References listed on IDEAS

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    1. Sabelfeld, K.K. & Mozartova, N.S., 2011. "Sparsified Randomization algorithms for low rank approximations and applications to integral equations and inhomogeneous random field simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 295-317.
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