Grobler, Jacobus Johannes2012-11-282012-11-282011Grobler, J.J. 2011. Doob's optional sampling theorem in Reisz spaces. Positivity, 15:617-637. [http://link.springer.com/journal/11117]1385-12921572-9281 (Online)http://hdl.handle.net/10394/7791Special issue in memoriam of Charalambos D. Aliprantis.The notions of stopping times and stopped processes for continuous stochastic processes are defined and studied in the framework of Riesz spaces. This leads to a formulation and proof of Doob’s optional sampling theorem.enStochastic process with continuous parametervector latticestopping timestopped processconditional expectationMartingale uniquenessArticle