Proportional growth with or without diffusion, and other explanations of scaling

Benoit B. Mandelbrot
Additional contact information
Benoit B. Mandelbrot: Yale University, Mathematics Department

Chapter E8 in Fractals and Scaling in Finance, 1997, pp 219-251 from Springer

Abstract: Abstract However useful and “creative” scaling may be, it is not accepted as an irreducible scientific principle. Several isolated instances of scaling are both unquestioned and easy to reduce to more fundamental principles, as will be seen in Section 1. There also exists a broad class of would-be universal explanations, many of them variants of proportional growth of U, with or without diffusion of log U. This chapter shows why, countering widely accepted opinion, I view those explanations as unconvincing and unacceptable. The models to be surveyed and criticized in this expository text were scattered in esoteric and repetitive references. Those I quote are the ear?liest I know. Many were rephrased in terms of the distribution of the sizes of firms. They are easily translated into terms of other scaling random variables that are positive. The two-tailed scaling variables that represent change of speculative prices (M 1963b{E14}) pose a different problem, since the logarithm of a negative change has no meaning.

Keywords: Random Walk; Firm Size; State Limit Function; Expository Text; Fire Damage (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-2763-0_8

Ordering information: This item can be ordered from
http://www.springer.com/9781475727630

DOI: 10.1007/978-1-4757-2763-0_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().