Browsing Faculty of Natural and Agricultural Sciences by Subject "Riesz space"

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    • Girsanov’s theorem in vector lattices 

      Grobler, Jacobus J.; Labuschagne, Coenraad C.A. (Springer, 2019)
      In this paper we formulate and proof Girsanov’s theorem in vector lattices. To reach this goal, we develop the theory of cross-variation processes, derive the cross-variation formula and the Kunita–Watanabe inequality. ...

    • 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, ...