Quadratic variation of martingales in Riesz spaces
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Grobler, Jacobus J.
Labuschagne, Coenraad C.A.
Marraffa, Valeria
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Elsevier
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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 Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales
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Grobler, J.J. et al. 2014. Quadratic variation of martingales in Riesz spaces. Journal of mathematical analysis and applications, 410:418-426. [https://doi.org/10.1016/j.jmaa.2013.08.037]