Open Access
2008 A martingale on the zero-set of a holomorphic function
Peter Kink
Author Affiliations +
Electron. Commun. Probab. 13: 606-613 (2008). DOI: 10.1214/ECP.v13-1425


We give a simple probabilistic proof of the classical fact from complex analysis that the zeros of a holomorphic function of several variables are never isolated and that they are not contained in any compact set. No facts from complex analysis are assumed other than the Cauchy-Riemann definition. From stochastic analysis only the Ito formula and the standard existence theorem for stochastic differential equations are required.


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Peter Kink. "A martingale on the zero-set of a holomorphic function." Electron. Commun. Probab. 13 606 - 613, 2008.


Accepted: 24 November 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60091
MathSciNet: MR2461534
Digital Object Identifier: 10.1214/ECP.v13-1425

Primary: 60H30
Secondary: 60G46 , 60H10

Keywords: Complex martingales , Stochastic differential equations

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