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August, 1977 Martingale Representations and Holomorphic Processes
R. Cairoli, J. B. Walsh
Ann. Probab. 5(4): 511-521 (August, 1977). DOI: 10.1214/aop/1176995757


We give a simple representation of two-parameter martingales in terms of a stochastic integral. This representation leads to the idea of the partial derivate of a martingale and to a generalization of the stochastic Green's theorem of the authors. Green's formula in this generalized form gives us a new and simpler proof of the fact that the derivative of a holomorphic process is holomorphic.


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R. Cairoli. J. B. Walsh. "Martingale Representations and Holomorphic Processes." Ann. Probab. 5 (4) 511 - 521, August, 1977.


Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0371.60068
MathSciNet: MR471078
Digital Object Identifier: 10.1214/aop/1176995757

Primary: 60H05
Secondary: 60G45

Keywords: holomorphic processes , Multiparameter martingales , Stochastic integrals in the plane

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 4 • August, 1977
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