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Random field representation and synthesis using wavelet bases. (English) Zbl 0886.65149
The authors address the representation and simulation of random fields using wavelet bases. The probabilistic description of the wavelet coefficients involved in the representation of the random field is discussed. It is shown that a broad class of random fields is amenable to a simplified representation. Further, it is shown that a judicious use of the local and multiscale structure of Daubéchies wavelets leads to an efficient simulation algorithm. The synthesis of random field samples is based on a wavelet reconstruction algorithm which can be associated with a dynamic system in the scale domain. Implementation aspects are considered and simulation errors are estimated. Examples of simulating random fields encountered in engineering applications are discussed.

65T60Wavelets (numerical methods)
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
42C40Wavelets and other special systems
60G60Random fields
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