The Annals of Probability

Additive Amarts

G. A. Edgar

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Abstract

Multi-parameter martingales and amarts can be studied using methods developed for amarts defined on a directed set by A. Millet and L. Sucheston. To study an amart indexed by $\mathbb{N} \times \mathbb{N}$, we use an associated process indexed by the "lower layers" of $\mathbb{N} \times \mathbb{N}$. J. B. Walsh's convergence theorem for two-parameter strong martingales is recovered as a special case. Vector-valued versions of some of the results are also stated.

Article information

Source
Ann. Probab., Volume 10, Number 1 (1982), 199-206.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993923

Digital Object Identifier
doi:10.1214/aop/1176993923

Mathematical Reviews number (MathSciNet)
MR637386

Zentralblatt MATH identifier
0492.60041

JSTOR
links.jstor.org

Subjects
Primary: 60G48: Generalizations of martingales

Keywords
Amart additive amart strong martingale stopping time stopping domain

Citation

Edgar, G. A. Additive Amarts. Ann. Probab. 10 (1982), no. 1, 199--206. doi:10.1214/aop/1176993923. https://projecteuclid.org/euclid.aop/1176993923


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