Transience of a pair of local martingales
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- by T. S. Mountford PDF
- Proc. Amer. Math. Soc. 103 (1988), 933-938 Request permission
Abstract:
We consider the process of windings of complex Brownian motion about two points $a$ and $b$ in the complex plane, $\{ ({\theta ^a}(t),{\theta ^b}(t)):t \geq 0\}$. We show that this process is transient in the sense that ${\lim _t} \to \infty |({\theta ^a}(t),{\theta ^b}(t))| = \infty$. This extends a result found in both Lyons and McKean (1984) and McKean and Sullivan (1984). We will mostly use facts and ideas found in the former paper.References
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- H. P. McKean and D. Sullivan, Brownian motion and harmonic functions on the class surface of the thrice punctured sphere, Adv. in Math. 51 (1984), no. 3, 203–211. MR 740581, DOI 10.1016/0001-8708(84)90006-9
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- H. P. McKean and D. Sullivan, Brownian motion and harmonic functions on the class surface of the thrice punctured sphere, Adv. in Math. 51 (1984), no. 3, 203–211. MR 740581, DOI 10.1016/0001-8708(84)90006-9
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 933-938
- MSC: Primary 60J65; Secondary 31B05, 60J45
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947686-5
- MathSciNet review: 947686