The Annals of Probability

Weak Martingales and Stochastic Integrals in the Plane

Eugene Wong and Moshe Zakai

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Abstract

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.

Article information

Source
Ann. Probab. Volume 4, Number 4 (1976), 570-586.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176996028

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176996028

Mathematical Reviews number (MathSciNet)
MR517927

Zentralblatt MATH identifier
0359.60053

Subjects
Primary: 60G45
Secondary: 60H05: Stochastic integrals

Keywords
Martingales 2-parameter processes stochastic integral random field Wiener process

Citation

Wong, Eugene; Zakai, Moshe. Weak Martingales and Stochastic Integrals in the Plane. Ann. Probab. 4 (1976), no. 4, 570--586. doi:10.1214/aop/1176996028. http://projecteuclid.org/euclid.aop/1176996028.


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