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
Grobler, J., Labuschagne, C., Marraffa, V. (2014). Quadratic Variation of Martingales in Riesz Spaces. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 410(1), 418-426 [10.1016/j.jmaa.2013.08.037].
Quadratic Variation of Martingales in Riesz Spaces
MARRAFFA, Valeria
2014-01-01
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
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