Now showing items 1-4 of 4

    • 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.
    • The Itô integral for Brownian motion in vector lattices. Part 2 

      Grobler, Jacobus J.; Labuschagne, Coenraad C.A. (Elsevier, 2015)
      The Itô integral for Brownian motion in a vector lattice, as constructed in Part 1 of this paper, is extended to accommodate a larger class of integrands. This extension provides an analogue of the indefinite Itô integral ...
    • The Itô integral for Brownian motion in vector lattices. Part1 

      Grobler, Jacobus J.; Labuschagne, Coenraad C.A. (Elsevier, 2015)
      In this paper the Itô integral for Brownian motion is constructed in a vector lattice and some of its properties are derived. The assumption is that there exists a conditional expectation operator on the vector lattice and ...
    • 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, ...