Now showing items 1-2 of 2

    • Doob's optional sampling theorem in Reisz spaces 

      Grobler, Jacobus Johannes (Springer, 2011)
      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.
    • Quadratic variation of martingales in Riesz spaces 

      Grobler, Jacobus J.; Labuschagne, Coenraad C.A.; Marraffa, Valeria (Elsevier, 2014)
      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, ...