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Computer Experiments With Fractional Gaussian Noises: Part 1, Averages and Variances
Author(s) -
Mandelbrot Benoit B.,
Wallis James R.
Publication year - 1969
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/wr005i001p00228
Subject(s) - usable , gaussian , sample (material) , statistical physics , gaussian process , mathematics , computer science , statistics , algorithm , mathematical optimization , physics , quantum mechanics , world wide web , thermodynamics
Fractional Gaussian noises are a family of random processes such that the interdependence between values of the process at instants of time very distant from each other is small but nonnegligible. It has been shown by mathematical analysis that such interdependence has precisely the intensity required for a good mathematical model of long run hydrological and geophysical records. This analysis will now be illustrated, extended, and made practically usable, with the help of computer simulations. In this Part, we shall stress the shape of the sample functions and the relations between past and future averages.