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A martingale on the zero-set of a holomorphic function


 
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1. Title Title of document A martingale on the zero-set of a holomorphic function
 
2. Creator Author's name, affiliation, country Peter Kink; Faculty for Computer and Information Sciences, University of Ljubljana
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) complex martingales; stochastic differential equations
 
3. Subject Subject classification 60H30;60G46;60H10;
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-11-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1425
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1425
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
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