Picard’s theorem and Brownian motion
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- by Burgess Davis
- Trans. Amer. Math. Soc. 213 (1975), 353-362
- DOI: https://doi.org/10.1090/S0002-9947-1975-0397900-8
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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
- Burgess Davis, On the distributions of conjugate functions of nonnegative measures, Duke Math. J. 40 (1973), 695–700. MR 324297
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
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- Avner Friedman, Wandering out to infinity of diffusion processes, Trans. Amer. Math. Soc. 184 (1973), 185–203. MR 341631, DOI 10.1090/S0002-9947-1973-0341631-5
- H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- 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