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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Transience of a pair of local martingales


Author: T. S. Mountford
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
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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 \vert({\theta ^a}(t),{\theta ^b}(t))\vert = \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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947686-5
Article copyright: © Copyright 1988 American Mathematical Society