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The Influence of Benoît B. Mandelbrot on Mathematics

Michael F. Barnsley, Michael Frame, Roger Howe, Ian Stewart, David Mumford, Hillel Furstenberg, Kenneth Falconer, Bruce J. West, Marc-Olivier Coppens, Nathan Cohen, Stéphane Jaffard, Michael Berry
2012 Notices of the American Mathematical Society  
The variety of these forms should be sampled by browsing through the illustrations.… -Benoît B. Mandelbrot [16, pp.  ...  Introduction We begin this article, which deals largely with Benoît B.  ... 
doi:10.1090/noti894 fatcat:s64gzh6d7nd33dv7aes2unue4i

Benoit B. Mandelbrot (1924–2010): a father of Quantitative Finance

M. A. H. Dempster
2011 Quantitative finance (Print)  
Financial Research, University of Cambridge & Cambridge Systems Associates Limited Benoit Mandelbrot was a father of Quantitative Finance in two senses.  ...  Benoit Mandelbrot was born in Warsaw on November 20 th 1924 into a family of scholars and mathematicians and died in Cambridge, Massachusetts on October 14 th 2010.  ... 
doi:10.1080/14697688.2011.552332 fatcat:ao3vqgz4jjb6pi2bhuu6cb766i

Correction [to "'Noah, Joseph, and operational hydrology' by Benoit B. Mandelbrot and James R. Wallis"]

1969 Water Resources Research  
The following corrections should be made in the paper 'Noah, Joseph, and Operational Hy drology' by Benoit B. Mandelbrot and James R. Wallis (Water Resources Research, 4(5), 1969).  ...  Correction The following corrections should be made in the paper 'Computer Experiments with Frac tional Gaussian Noises' by Benoit B. Mandel brot and James R.  ... 
doi:10.1029/wr005i005p01164-01 fatcat:n5nmuzs4ezfqzgnmqsjc6mbzie

Fractais [chapter]

Benoît B. Mandelbrot
2003 Fronteiras da Ciência: desenvolvimentos recentes, desafios futuros  
Fractais Autor(es): Mandelbrot, Benoît B.  ...  Lovejoy e B. B. Mandelbrot) Fig. 3 - 3 Fragmento muito pequeno do conjunto de Mandelbrot (R. F Voss) Fig. 4 - 4 Pequeno fragm ento do conjuntode Mandelbrot modificado (B. B.  ...  Mandelbrot) Fig. 12 - 12 Conjunto de Mandelbrot, rodeado pelas suas curvas equipotenciais (B. B. Mandelbrot) Eis como o conjunto M se constrói.  ... 
doi:10.14195/978-989-26-0389-6_5 fatcat:xvmv5b4mibeglnuavaooufcpu4

The variation of certain speculative prices [chapter]

Benoit B. Mandelbrot
1997 Fractals and Scaling in Finance  
Soc. (1961), pp. 157-61. 7 Benoit Mandelbrot, "The Pareto-L6vy Law and the Distribution of Income," International Economic Review, I (1960), 79-106, as amended in "The Stable Paretian Income Distribution  ...  B.  ... 
doi:10.1007/978-1-4757-2763-0_14 fatcat:qaj4qgrz6fcaxdo6equdywax6a

Parallel cartoons of fractal models of finance

Benoit B. Mandelbrot
2005 Annals of Finance  
While B(t) itself is additive, this variant is a multiplicative recursive process the author calls a "cartoon."  ...  The argument builds on a technical wrinkle (used earlier but explained here fully for the first time), namely, the author's grid-bound variant of Brownian motion B(t).  ...  A second more important difference is that in PLM those discontinuities are not "fixes" added by hand to correct a defect of B(t).  ... 
doi:10.1007/s10436-004-0007-2 fatcat:kqgtpwq4srdttegr7e3ganxzyu

Towards a Second Stage of Indeterminism in Science

Benoit B. Mandelbrot
1987 Interdisciplinary Science Reviews  
B. B. Mandelbrot: It occupies a critical position along the tortuous path that eventually led to fractals.  ...  One cannot always expect the causal reduction of fluctuations described under B to be possible.  ... 
doi:10.1179/030801887789799213 fatcat:s25o3vn3pvbulc6dtatqvgheiy

Inversion Formula for Continuous Multifractals

Rudolf H Riedi, Benoit B Mandelbrot
1997 Advances in Applied Mathematics  
. < < exponent exponent ␣ B s log B rlog B roughly equal to ␣.''  ...  Let H be the set of all intervals B s l␦ , l q 1 ␦ with integer l and ␦ Ž . wŽ . Ž . . with B / 0, and let B [ l y 1 ␦, l q 2 ␦ . Then 1 < < ␣q < < ␣y N ␣, s࠻ BgH : B F B -B . Ä 4 Ž .  ... 
doi:10.1006/aama.1997.0550 fatcat:3rrwnhrihbfyxe2foksuwxb5vq

Fractals and an Art for the Sake of Science

Benoit B. Mandelbrot
1989 Leonardo Supplemental Issue  
This happened with my first book in 1975 [2] Mandelbrot, Fractals and an Art for the Sake of Science  ... 
doi:10.2307/1557938 fatcat:q7vhtsx47zgjvl5mcivqvgen2i

Towards a Second Stage of Indeterminism in Science

Benoit B. Mandelbrot
1987 Interdisciplinary Science Reviews  
B. B. Mandelbrot: It occupies a critical position along the tortuous path that eventually led to fractals.  ...  One cannot always expect the causal reduction of fluctuations described under B to be possible.  ... 
doi:10.1179/isr.1987.12.2.117 fatcat:eka33sqcojdevbnapen7xnm6ze

Some long-run properties of geophysical records

Benoit B. Mandelbrot, James R. Wallis
1969 Water Resources Research  
IV Indien men met behulp van de empirische samenhang tussen (a) de onderlinge afstand tussen neerslagwaarnemingsstations en (b) de correlatie tussen neerslaghoeveelheden in dezelfde tijdvakken gemeten,  ...  BENOIT B. MANDELBROT and JAMES R. WALLIS. Some Long-Run TE CHOW (1964), 8-I-IIC3): JV _ NjT^l ; ?  ...  Therefore, the gfs V(s) of {v"}, B(s) of {b"} and £/(s) are related by (see Appendix Al): (2.28) V(s) = B(s)U(s) = B(s)/(l-F(s)) (cf.  ... 
doi:10.1029/wr005i002p00321 fatcat:hsmfhq334bclrducdxe6ihda7e

Stable fractal sums of pulses: the cylindrical case

Renata Cioczek-Georges, Benoit B. Mandelbrot, Gennady Samorodnitsky, Murad S. Taqqu
1995 Bernoulli  
Mandelbrot, G.  ...  Mandelbrot (1995) .  ... 
doi:10.3150/bj/1193667815 fatcat:4c2jrex3tncanpu543wbsf7wlm

Inverse Measures, the Inversion Formula, and Discontinuous Multifractals

Benoit B Mandelbrot, Rudolf H Riedi
1997 Advances in Applied Mathematics  
␣y 1r␣ , the straight line y s A␣ q B becomes the straight line y* s Ž . A q B␣. Therefore, the well-known inequality f ␣ F 1 implies f * F ␣. Ž . Ž .  ...  This is not the place to describe in full the general theory of random multifractals presented by Mandelbrot w x M89, M90, M95 .  ... 
doi:10.1006/aama.1996.0500 fatcat:xttahar4k5hdbf7r3cozmbusw4

Heavy Tails in Finance for Independent or Multifractal Price Increments [chapter]

Benoit B. Mandelbrot
2003 Handbook of Heavy Tailed Distributions in Finance  
To the contrary, one of the key features of the multifractals (Mandelbrot, 1974a, b) remains little known.  ...  But Mandelbrot (1974a, b) also allows for an alternative possibility, which has so far remained little known.  ... 
doi:10.1016/b978-044450896-6.50003-0 fatcat:fvydikxm25f53lwqfpkmffmci4

Correction of an Error in "The Variation of Certain Speculative Prices" (1963)

Benoit B. Mandelbrot
1972 The journal of business  
Benoit B.  ...  Mandelbrot Correction of an Error in “The Variation of Certain Speculative Prices” (1963) I have found an error in my paper, “The Variation of Certain Specula- tion Prices,” which first appeared in this  ... 
doi:10.1086/295487 fatcat:hndj6zt6pjh2tlm56t6ka5hmiq
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