Brownian motion on the figure eight

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


In an interval containing the origin we study a Brownian motion which returns to zero as soon as it reaches the boundary. We determine explicitly its transition probability, prove it is ergodic and calculate the decay rate to equilibrium. It is shown that the process solves the martingale problem for certain asymmetric boundary conditions and can be regarded as a diffusion on an eight shaped domain. In the case the origin is situated at a rationally commensurable distance from the two endpoints of the interval we give the complete characterization of the possibility of collapse of distinct paths.

Original languageEnglish (US)
Pages (from-to)817-844
Number of pages28
JournalJournal of Theoretical Probability
Issue number3
StatePublished - 2002


  • Absorbing Brownian motion
  • Decay rate
  • Ergodicity
  • Laplace transform

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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