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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Picard's theorem and Brownian motion


Author: Burgess Davis
Journal: Trans. Amer. Math. Soc. 213 (1975), 353-362
MSC: Primary 60J65; Secondary 30A70
DOI: https://doi.org/10.1090/S0002-9947-1975-0397900-8
MathSciNet review: 0397900
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Abstract: Properties of the paths of two dimensional Brownian motion are used as the basis of a proof of the little Picard theorem and its analog for complex valued functions, defined on simply connected n dimensional manifolds, which map certain diffusions into Brownian motion.


References [Enhancements On Off] (What's this?)

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  • [3] J. L. Doob, Semimartingales and subharmonic functions, Trans. Amer. Math. Soc. 77 (1954), 86-121. MR 16, 269. MR 0064347 (16:269a)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0397900-8
Keywords: Picard theorem, Brownian motion, diffusion processes
Article copyright: © Copyright 1975 American Mathematical Society

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