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A Fast Fractional Gaussian Noise Generator
Author(s) -
Mandelbrot Benoit B.
Publication year - 1971
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr007i003p00543
Subject(s) - gaussian , hierarchy , simple (philosophy) , gaussian noise , generator (circuit theory) , extension (predicate logic) , noise (video) , gauss , mathematics , variable (mathematics) , statistical physics , markov chain , computer science , algorithm , statistics , mathematical analysis , physics , artificial intelligence , power (physics) , quantum mechanics , image (mathematics) , philosophy , epistemology , economics , market economy , programming language
By design fast fractional Gaussian noises (ffGn) have the following characteristics: The number of operations needed to generate them is relatively small. The long run statistical dependence that they exhibit is strong and has the form required for self similar hydrology. Their short run properties, as expressed by the correlations between successive or nearly successive yearly averages, are adjustable (within bounds) and can be fitted to the corresponding short run properties of records. Extension to the multidimensional (multisite) case should raise no essential difficulty. Finally, their definition, as sums of Markov‐Gauss and other simple processes, fits the intuitive ideas that climate can be visualized as either unpredictably inhomogeneous or ruled by a hierarchy of variable regimes.