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Brownian Motion: Local Distributions

  • David Aldous
Part of the Applied Mathematical Sciences book series (AMS, volume 77)

Abstract

This opaque title means “distributions related to local sample path properties of Brownian motion”. I have in mind properties such as Lévy’s estimate of the modulus of continuity, the corresponding results on small increments, the paradoxical fact that Brownian motion has local maxima but not points of increase, and self-intersection properties in d dimensions. Although these are “0–1” results, they can be regarded as consequences of stronger “distributional” assertions which can easily be derived via our heuristic. The topics of this section are more theoretical than were previous topics, though many are equivalent to more practical-looking problems on boundary-crossing.

Keywords

Brownian Motion Sojourn Time Local Distribution Small Increment Standard Brownian Motion 
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 Science+Business Media New York 1989

Authors and Affiliations

  • David Aldous
    • 1
  1. 1.Department of StatisticsUniversity of California-BerkeleyBerkeleyUSA

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