Brownian Motion on the Figure Eight

Ilie Grigorescu () and Min Kang ()
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Ilie Grigorescu: University of Miami
Min Kang: Northwestern University

Journal of Theoretical Probability, 2002, vol. 15, issue 3, 817-844

Abstract: 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.

Keywords: Absorbing Brownian motion; Laplace transform; decay rate; ergodicity (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1016232201962

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