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A martingale on the zero-set of a holomorphic function

   
@article{ECP1425,
	author = {Peter Kink},
	title = {A martingale on the zero-set of a holomorphic function},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {complex martingales; stochastic differential equations},
	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.},
	pages = {no. 55, 606-613},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1425},    
        url = {http://ecp.ejpecp.org/article/view/1425}}