Nevanlinna Theory and Stochastic Calculus
Several relationships between classical function theory and analysis of Brownian motion have been studied by many authors (cf. , ). Davis gave an elegant proof of Picard’s theorem in  which impressed us with their intimacy. It also gave some possibility to study value-distribution of meromorphic functions through Brownian motion or stochastic calculus. It is curious that there had been no article noting a simple relation between Nevanlinna theory and Brownian motion until Carne’s paper . He considered some probabilistic aspects of classical Nevanlinna theory. After the work the author improved it to several dimensional cases in . In this note we exemplify this natural relation between stochastic calculus and Nevanlinna theory by considering a stochastic generalization of first main theorem of Nevanlinna and its applications.
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