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On Convergence of Vector valued Pramarts and Subpramarts

Published online by Cambridge University Press:  20 November 2018

Nikos E. Frangos
Nikos E. Frangos*
Affiliation:
The Ohio State University, Columbus, Ohio
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In [15] Millet and Sucheston introduced the notion of pramart and subpramart indexed by directed sets, generalizing that of martingale and submartingale, and studied their properties. In particular convergence theorems were proved. In this note we obtain convergence theorems for analogous Banach-valued processes.

Let E be a Banach lattice with the Radon-Nikodym property. Let (Xt, , t ∊ J) be an E+-valued subpramart of class (d). Precise definitions are given below (Section 1).

In [10] for J = N, Egghe proved a subpramart convergence theorem under the additional assumption that there is a subsequence {nk} ⊆ N such that converges weakly for each .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 2 , 01 April 1985 , pp. 260 - 270
Copyright
Copyright © Canadian Mathematical Society 1985

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