Brownian motion on the figure eight

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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
Volume15
Issue number3
DOIs
StatePublished - 2002

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Brownian motion
Figure
Martingale Problem
Interval
Transition Probability
Decay Rate
Distinct
Boundary conditions
Calculate
Path
Zero
Transition probability
Decay
Martingale

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Brownian motion on the figure eight. / Grigorescu, Ilie; Kang, Min.

In: Journal of Theoretical Probability, Vol. 15, No. 3, 2002, p. 817-844.

Research output: Contribution to journalArticle

Grigorescu, Ilie ; Kang, Min. / Brownian motion on the figure eight. In: Journal of Theoretical Probability. 2002 ; Vol. 15, No. 3. pp. 817-844.
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