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