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Quadratic variation of martingales in Riesz spaces |
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| Authors: | Jacobus J. Grobler Coenraad C.A. Labuschagne Valeria Marraffa |
| Affiliation: | 1. School for Computer, Statistical and Mathematical Sciences, North-West University, South Africa;2. School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, South Africa1;3. Department of Finance and Investment Management, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa2;4. Dipartimento di Matematica e Informatica, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy |
| Abstract: | We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austin?s sample function theorem, on convergence of the quadratic variation processes of martingales. |
| Keywords: | Austin?s theorem Martingale Measure-free stochastic processes Quadratic variation Riesz space Vector lattice |
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