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February, 1982 Additive Amarts
G. A. Edgar
Ann. Probab. 10(1): 199-206 (February, 1982). DOI: 10.1214/aop/1176993923

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.

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G. A. Edgar. "Additive Amarts." Ann. Probab. 10 (1) 199 - 206, February, 1982. https://doi.org/10.1214/aop/1176993923

Information

Published: February, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0492.60041
MathSciNet: MR637386
Digital Object Identifier: 10.1214/aop/1176993923

Subjects:
Primary: 60G48

Keywords: additive amart , Amart , stopping domain , stopping time , strong martingale

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February, 1982
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