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

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

Monte Carlo Methods and Applications, 2017, vol. 23, issue 3, 165-188

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.

Keywords: Karhunen–Loève series; Monte Carlo; orthonormal systems and bases; parametric models; stochastic dimension; vector-valued random functions (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1515/mcma-2017-0112

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