Grobler, Jacobus2016-01-262016-01-262014Grobler, J. 2014. Jensen’s and martingale inequalities in Riesz spaces. Indagationes mathematicae, 25(2):275-295. [https://doi.org/10.1016/j.indag.2013.02.003]0019-3577http://hdl.handle.net/10394/16032https://doi.org/10.1016/j.indag.2013.02.003https://www.sciencedirect.com/science/article/pii/S0019357713000141A functional calculus is defined and used to prove Jensen’s inequality for conditional expectations acting on Riesz spaces. Upcrossing inequalities, martingale inequalities and Doob’s L p-inequality for continuous time martingales and submartingales are provedenVector latticeStochastic processJensen’s inequalityDoob’s L p-inequalityDoob’s maximal inequalityUpcrossing theoremDowncrossing theoremArticle