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*EP
Photographs of three “seed” papersin French: M 1951, M 1962c,
and M 1965h{H9}
This page serves as preface to ten added pages of strictly
historical interest.
From the 1950s to the 1970s, I presented French
announcements-summaries of my main English articles to the Comptes
rendus de l'Académiedes Sciences de Paris. Three of these "Notes"
concern the following topics:"power-law" distributions,
long-tailedness in finance, and long dependencein the real world.
No one else was interested in those topics, hence theseNotes were
the first – by long periods of time – in applying
sophisticatedmathematical modeling in those contexts. Today the
originals are oftenquoted but were not available in a book in
English, motivating the photo-graphs that follow. The pages had to
be slightly reduced in size.
M 1951 explained Zipf's law of word frquencies, once and for
all. M1962c introduced and clearly described the key idea of the
PLM(mesofractal) model of price variation. M 1965h introduced and
clearlydescribed the key idea of the HHM (unifractal) model. The
last twopapers led to the fractal/scaling approach to finance.
They have aged well and are now described as path-breaking or
asseed papers. Of course they were limited to the basic ideas
stated tersely– but clearly. Nevertheless, hard work spanning
nearly fifty or at leastnearly forty years was needed to develop
them to the point of presentwide acceptance.
Previous reproductions of these papers are found in M 1997FE.
Partof M 1962c is translated in Section 6.1 of the Introduction of
M 1997E. M1965h is translated as Chapter H9 of M 2002H, which
includes an anno-tation explaining the entirely inappropriate term
“homothétique à soi”
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2 FRACTALS AND SCALING IN FINANCE ♦ ♦ *EP
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*EP ♦ ♦ THREE SEED PAPERS (1951, 1962, 1965) 3
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4 FRACTALS AND SCALING IN FINANCE ♦ ♦ *EP
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*EP ♦ ♦ THREE SEED PAPERS (1951, 1962, 1965) 5
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6 FRACTALS AND SCALING IN FINANCE ♦ ♦ *EP
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*EP ♦ ♦ THREE SEED PAPERS (1951, 1962, 1965) 7
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8 FRACTALS AND SCALING IN FINANCE ♦ ♦ *EP
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*EP ♦ ♦ THREE SEED PAPERS (1951, 1962, 1965) 9
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10 FRACTALS AND SCALING IN FINANCE ♦ ♦ *EP
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*EP ♦ ♦ THREE SEED PAPERS (1951, 1962, 1965) 11
Comments and errata. This paper describes the fractional
integration ituses as due to Riemann and Liouville. However, it
does not: thatexpression uses an integral from 0 to t and would
have led into adead-end. To avoid it, and without saying anything,
I used an integralfrom − ∞ to t. Not known to me at that time, this
variant is due toHermann Weyl. In the formula that follows, the
term in [ ] should be[|v − ε|2H − 2v2H + (v + ε)2H]. A paper
referenced in Note 3 was delayed,appeared as M 1965c, and is
reprinted as Chapter N7 of M 1999N. Open-ended references can be
filled by referring to the Vita on my website.
