A martingale on the zero-set of a holomorphic function
Peter Kink, Faculty for Computer and Information Sciences, University of Ljubljana
Abstract
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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