Nevanlinna Theory via Stochastic Calculus

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Abstract

We study Nevanlinna theory using stochastic calculus. We have a defect relation for holomorphic maps in equidimensional cases which includes Carlson and Griffiths′ defect relation. The main probabilistic methods used here are some estimates on some increasing processes for Brownian motion and martingales on manifolds. The latter is obtained from Krylov′s estimate on stochastic integrals for martingales.

Original languageEnglish
Pages (from-to)473-510
Number of pages38
JournalJournal of Functional Analysis
Volume132
Issue number2
DOIs
Publication statusPublished - 1995 Jan 1

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ASJC Scopus subject areas

  • Analysis

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