Amarts on Riesz spaces |
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Authors: | Wen Chi Kuo Coenraad C. A. Labuschagne Bruce A. Watson |
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Affiliation: | (1) School of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050 Witwatersrand, South Africa |
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Abstract: | The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math., 15 (2004), 435–451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced. Supported in part by the John Knopfmacher Centre for Applicable Analysis and Number Theory |
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Keywords: | amart martingale Riesz space Banach lattice |
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