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Multiscaling and random cascades

Published online by Cambridge University Press:  01 July 2016

Edward C. Waymire
Edward C. Waymire*
Affiliation:
Oregon State University
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Extract

The study of spatial distributions which arise from independent multiplicative cascades can be traced back at least to the efforts by the Russian school led by Andrei N. Kolmogorov on the statistical theory of turbulence. However, largely owing to the intriguing statistical/geometric scaling properties so heavily emphasized by Benoit Mandelbrot, and to the rich mathematical foundations begun by Jean-Pierre Kahane and Jacques Peyriere in the middle 1970's and continuing to the present, there has been a growing interest in random cascades both in the physical sciences and in mathematics. Our objective is to review some of the principal aspects of the theory and applications of independent cascades as well as some recent extensions.

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 343 - 344
Copyright
Copyright © Applied Probability Trust 1996 

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References

Gupta, V. K. and Waymire, Ε. C. (1993) A statistical analysis of mesoscale rainfall as a random cascade. J. Appl. Meteorol. 12, 251–267.2.0.CO;2>CrossRefGoogle Scholar
Holley, R. and Waymire, E. (1992) Multifractal dimensions and scaling exponents for strongly bounded random cascades. Ann. Appl. Prob. 2, 819–845.CrossRefGoogle Scholar
Kahane, J. P. and Peyriere, (1976) Sur certaines martingales de Benoit Mandelbrot. Adv. Math. 22, 131–145.CrossRefGoogle Scholar
She, Z. S. and Waymire, E. C. (1995) Quantized energy cascade and log-Poisson statistics in fully developed turbulence. Phys. Rev. Lett. 74, 262–265.CrossRefGoogle ScholarPubMed
Waymire, E. and Williams, S. (1994) A general decomposition theory for random cascades. Bullet. Amer. Math. Soc. 31, 216–222.CrossRefGoogle Scholar
Waymire, E. and Williams, S. (1995) Multiplicative cascades: dimension spectra and dependence, J. Fourier Anal. Appl. (special issue), 589–609.Google Scholar
Waymire, E. and Williams, S. (1995) A cascade decomposition theory with applications to Markov and exchangeable cascades. Trans. Amer. Math. Soc. (in press).CrossRefGoogle Scholar