6533b873fe1ef96bd12d5719

RESEARCH PRODUCT

Quadratic variation of martingales in Riesz spaces

J. J. GroblerValeria MarraffaCoenraad C.a. LabuschagneCoenraad C.a. Labuschagne

subject

Discrete mathematicsPure mathematicsRiesz potentialRiesz representation theoremApplied MathematicsmartingaleRiesz spaceRiesz spacevector latticeQuadratic variationquadratic variationM. Riesz extension theoremSettore MAT/05 - Analisi MatematicaAustin’s theorem Martingale Measure-free stochastic processes Quadratic variation Riesz space Vector latticemeasure-free stochastic processesAustinʼs theoremMartingale (probability theory)AnalysisMathematics

description

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 http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)

yearjournalcountryeditionlanguage
2014-02-01
https://hdl.handle.net/10394/16394