Fractals and Scaling in Finance
Fractals and Scaling in Finance
复制标题
DOI：
10.1007/978-1-4757-2763-0
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
B. Mandelbrot
中科院分区：
文献类型：
--
作者：
B. Mandelbrot
1959年至1961年，在约克敦高地，沙里宁设计的大型研究实验室正在建造中，IBM的大部分研究室都设在附近。我们一伙人住在兰姆庄园的一栋小房子里，那里曾是一家疗养院，住着有钱的酒鬼。下面这张照片拍摄于1960年。它显示从右到左，T。e.现在在圣巴巴拉的加州大学。我是下一个，盯着我刚刚写在黑板上的网络。然后是保罗吉尔摩，已故的不列颠哥伦比亚省大学，然后（坐）理查德莱维坦，现在退休，在左边是伯努瓦曼德尔布罗特。x前言EF即使在一个兰姆庄园里，只有聪明的研究人员，伯努瓦总是脱颖而出。他的思想总是新鲜的，我喜欢和他谈论任何主题，无论是技术，政治还是历史。他向我介绍了这样一种想法，即具有无限二阶矩的分布不仅仅是数学上的好奇心和反例的来源。这是一种思想路线的预示，最终导致了分形和物理世界的主要部分可以，事实上只能，由具有分数维的分布和集合建模的概念。通常，这些分布和集合被数学家们所熟知，就像我所知道的那样，作为好奇心和反直觉的例子，用来向研究生们展示证明的严谨性。
IN 1959-61, while the huge Saarinen-designed research laboratory at Yorktown Heights was being built, much of IBM's Research was housed nearby. My group occupied one of the many little houses on the Lamb Estate complex which had been a sanatorium housing wealthy alcoholics. The picture below was taken about 1960. It shows from right to left, T. e. Hu, now at the University of California, Santa Barbara. I am next, staring at a network I have just written on the blackboard. Then comes Paul Gilmore, late of the University of British Columbia, then (seated) Richard Levitan, now retired, and at the left is Benoit Mandelbrot. x FOREWORD EF Even in a Lamb Estate populated exclusively with bright research oriented people, Benoit always stood out. His thinking was always fresh, and I enjoyed talking with him about any subject, whether technical, poli tical, or historical. He introduced me to the idea that distributions having infinite second moments could be more than a mathematical curiosity and a source of counter-examples. This was a foretaste of the line of thought that eventually led to fractals and to the notion that major pieces of the physical world could be, and in fact could only be, modeled by distrib utions and sets that had fractional dimensions. Usually these distributions and sets were known to mathematicians, as they were known to me, as curiosities and counter-intuitive examples used to show graduate students the need for rigor in their proofs.