A multivariate Weierstrass–Mandelbrot function
1985 ◽
Vol 400
(1819)
◽
pp. 331-350
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Keyword(s):
The Many
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The univariate Weierstrass–Mandelbrot function is generalized to many variables to model higher dimensional stochastic processes such as undersea topography. Because this topography is difficult to measure at small length scales over the many large regions that affect long-ranged acoustic propagation in the ocean, one needs a stochastic description that can be extrapolated to both large and small features. Fractal surfaces are a convenient framework for such a description. Computer-generated plots for the two-variable case are presented. It is shown that in the continuum limit the multivariate function is equivalent to the multivariate fractional Brownian motion.
2000 ◽
Vol 14
(12n13)
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pp. 1399-1420
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2020 ◽
Vol 35
(17)
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pp. 2050079
2012 ◽
Vol 2012
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pp. 1-14
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Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications
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1996 ◽
Vol 1996
(0)
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pp. 47-52
2012 ◽
Vol 15
(1)
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1993 ◽
Vol 39
(1)
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pp. 260-264
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