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Fractional Brownian Motions, Fractional Noises and Applications

Authors: Benoit B. Mandelbrot and John W. Van NessAuthors Info & Affiliations
https://doi.org/10.1137/1010093
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References

1.
I. Adelman, Long cycles—fact or artifact?, Amer. Economic Rev., 60 (1965), 444–463
Google Scholar
2.
William Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Statistics, 22 (1951), 427–432
Crossref
Web of Science
Google Scholar
3.
I. M. Gel'fand, N. Ya. Vilenkin, Generalized functions. Vol. 4, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1964 [1977]xiv+384
Google Scholar
4.
C. W. J. Granger, The typical spectral shape of an economic variable, Econometrica, 34 (1966), 150–161
Crossref
Web of Science
Google Scholar
5.
G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc., 71 (1951), 38–69
Crossref
Web of Science
Google Scholar
6.
H. E. Hurst, R. P. Black, Y. M. Sinaika, Long Term Storage in Reservoirs. An Experimental Study, Constable, London, 1965
Google Scholar
7.
A. N. Kolmogoroff, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. Sci. URSS (N.S.), 26 (1940), 115–118
Google Scholar
8.
John Lamperti, Semi-stable stochastic processes, Trans. Amer. Math. Soc., 104 (1962), 62–78
Crossref
Google Scholar
9.
Paul Lévy, Random functions: General theory with special reference to Laplacian random functions, Univ. California Publ. Statist., 1 (1953), 331–390
Google Scholar
10.
Michel Loève, Probability theory, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960xvi+685
Google Scholar
11.
Benoı⁁t Mandelbrot, Une classe processus stochastiques homothétiques à soi; application à la loi climatologique H. E. Hurst, C. R. Acad. Sci. Paris, 260 (1965), 3274–3277
Google Scholar
12.
B. Mandelbrot, Self-similar error-clusters in communication systems and the concept of conditional stationarity, IEEE Trans. Comet. Tech., COM-13 (1965), 71–90
Crossref
Web of Science
Google Scholar
13.
B. Mandelbrot, Noises with an $l/f$ spectrum, a bridge between direct current and white noise, IEEE Trans. Information Theory, IT-13 (1967), 289–298
Crossref
Web of Science
Google Scholar
14.
Benoit Mandelbrot, Sporadic random functions and conditional spectral analysis: Self-similar examples and limitsProc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), Vol. III: Physical Sciences, Univ. California Press, Berkeley, Calif., 1967, 155–179
Google Scholar
15.
B. Mandelbrot, J. R. Wallis, Noah, Joseph and operational hydrology, Water Resources Research, to appear
Google Scholar
16.
B. Mandelbrot, J. R. Wallis, Computer experiments with fractional Gaussian noise, Water Resources Research, to appear
Google Scholar
17.
B. Mandelbrot, J. R. Wallis, Some long run properties of geophysical records, Water Resources Research, to appear.
Google Scholar
18.
G. Maruyama, The harmonic analysis of stationary stochastic processes, Mem. Fac. Sci. Kyusyu Univ. A., 4 (1949), 45–106
Crossref
Google Scholar
19.
M. Rosenblatt, Independence and dependenceProc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, 431–443
Google Scholar
20.
G. I. Taylor, Statistical theory of turbulence, Proc. Roy. Sac. Ser. A, 151 (1935), 421–478
Crossref
Google Scholar
21.
H. Weyl, Bemerkungen zum Begriff der Differential-Quotenten gebrochener Ordnung, Vierteljschr. Naturforsch. Ges. Zürich, 62 (1967), 296–302
Google Scholar
22.
A. M. Yaglom, Correlation theory of processes with random stationary nth increments, Amer. Math. Soc. Transl. (2), 8 (1958), 87–141
Crossref
Google Scholar
23.
A. M. Yaglom, L. M. LeCam, J. Neyman, Stationary Gaussian processes satisfying the strong mixing condition and best predictable functionalsBernoulli-Bayes-Laplace Anniversary Volume, Springer-Verlag, New York, 1965, 241–252
Crossref
Google Scholar
24.
A. M. Yaglom, Outline of some topics in linear extrapolation of stationary random processesProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II:Contributions to Probability Theory, Part 1, Univ. California Press, Berkeley, Calif., 1967, 259–278
Google Scholar
25.
Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952vi+329, 2nd ed.
Google Scholar

Information & Authors

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Published In

cover image SIAM Review
SIAM Review
Volume 10 • Issue 4 • October 1968
Pages: 422 - 437
DOI: 10.1137/1010093
ISSN (online): 1095-7200

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Copyright © 1968 Society for Industrial and Applied Mathematics.

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Submitted: 11 December 1967
Published online: 18 July 2006

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