Abstract
Several relationships between classical function theory and analysis of Brownian motion have been studied by many authors (cf. [9], [5]). Davis gave an elegant proof of Picard’s theorem in [8] 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 [6]. He considered some probabilistic aspects of classical Nevanlinna theory. After the work the author improved it to several dimensional cases in [1]. 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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Atsuji, A. (2000). Nevanlinna Theory and Stochastic Calculus. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0269-8_50
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DOI: https://doi.org/10.1007/978-1-4613-0269-8_50
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