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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 ...
    • Jensen’s and martingale inequalities in Riesz spaces 

      Grobler, Jacobus (Elsevier, 2014)
      A 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 ...
    • The quadratic variation of continuous time stochastic processes in vector lattices 

      Grobler, Jacobus J.; Labuschagne, Coenraad C.A. (Elsevier, 2017)
      We define and study order continuity, topological continuity, γ-Hölder-continuity and Kolmogorov–Čentsov-continuity of continuous-time stochastic processes in vector lattices and show that every such kind of continuous ...