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

Hunt Tame 

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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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