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August, 1976 Weak Martingales and Stochastic Integrals in the Plane
Eugene Wong, Moshe Zakai
Ann. Probab. 4(4): 570-586 (August, 1976). DOI: 10.1214/aop/1176996028


This paper continues the development of a stochastic calculus for two-parameter martingales, and particularly for the two-parameter Wiener process. Whereas in an earlier paper we showed that two types of stochastic integrals were necessary for representing functionals and martingales of a Wiener process, introduction of two mixed area integrals is necessary to complete the stochastic calculus. These mixed integrals are weak martingales in the sense of Cairoli and Walsh, and are necessary in a general representation for weak martingales and transformations of weak martingales. Stopping times are introduced for two-parameter processes, and a characterization of strong martingales in terms of stopping times is given.


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Eugene Wong. Moshe Zakai. "Weak Martingales and Stochastic Integrals in the Plane." Ann. Probab. 4 (4) 570 - 586, August, 1976.


Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0359.60053
MathSciNet: MR517927
Digital Object Identifier: 10.1214/aop/1176996028

Primary: 60G45
Secondary: 60H05

Keywords: 2-parameter processes , Martingales , Random field , stochastic integral , Wiener process

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 4 • August, 1976
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