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April, 1981 Some Classes of Two-Parameter Martingales
Moshe Zakai
Ann. Probab. 9(2): 255-265 (April, 1981). DOI: 10.1214/aop/1176994466


A class of two-parameter martingales, named "martingales with orthogonal increments" or "martingales of direction independent variation," is introduced. It is shown that this class, which is characterized by a sample function property, is included in the class of martingales of path independent variation and includes the class of strong martingales. The class of martingales with orthogonal increments is stable under stochastic integration and some results, which were obtained previously for strong martingales, hold also for martingales with orthogonal increments. It is shown that if $M_z$ is a martingale with orthogonal increments on the sigma-fields generated by the Wiener process then there exists a Wiener process such that $M_z$ can be represented as a stochastic integral of first type with respect to it.


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Moshe Zakai. "Some Classes of Two-Parameter Martingales." Ann. Probab. 9 (2) 255 - 265, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0462.60055
MathSciNet: MR606987
Digital Object Identifier: 10.1214/aop/1176994466

Primary: 60H05
Secondary: 60G45

Keywords: martingales of orthogonal increments , Multiparameter martingales , stable subspaces of martingales

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 2 • April, 1981
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