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Richness of Paths

  • J. Michael Steele
Part of the Applications of Mathematics book series (SMAP, volume 45)

Abstract

One could spend a lifetime exploring the delicate — and fascinating — properties of the paths of Brownian motion. Most of us cannot afford such an investment, so hard choices must be made. Still, without any doubt, there are two fundamental questions that must be considered to a reasonable depth:
  • How smooth — or how rough — is a Brownian path?

  • How do the paths of Brownian motion relate to those of random walk?

Keywords

Brownian Motion Random Walk Central Limit Theorem Wavelet Coefficient Invariance Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • J. Michael Steele
    • 1
  1. 1.The Wharton School, Department of StatisticsUniversity of PennsylvaniaPhiladelphiaUSA

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