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The standard Brownian motion

  • Kiyosi Itô
  • Henry P. McKeanJr.
Part of the Classics in Mathematics book series (CLASSICS)

Abstract

Consider a person walking in the integers according to the following rule: start at time n = 0 at s(0) = 0, ±1, ± 2 , . . . and flip a true coin; if tails comes up, step at time n = 1 to s(1) = s(0) - 1; if heads comes up, step to s(l) = s(0) + l. Coming, thus, at time n - 1 to s(n - 1), flip the coin; if tails comes up, step at time n to s(n) = s(n - 1) - 1, if heads comes up, step to s(n)= s(n - 1) + 4; etc.

Keywords

BRowNian Motion Passage Time Sample Path Lower Class Iterate Logarithm 
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 Berlin Hiedelberg 1996

Authors and Affiliations

  • Kiyosi Itô
    • 1
    • 3
  • Henry P. McKeanJr.
    • 2
  1. 1.RIMSKyoto UniversitySakyo-Ku, KyotoJapan
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Cornell UniversityUSA

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