Now showing items 1-5 of 5

    • 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. 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 ...
    • The Kolmogorov–Čentsov theorem and Brownian motion in vector lattices 

      Grobler, J.J. (Elsevier, 2014)
      The well known Kolmogorov–Čentsov theorem is proved in a Dedekind complete vector lattice (Riesz space) with weak order unit on which a strictly positive conditional expectation is defined. It gives conditions that guarantee ...
    • A note on Brownian areas and arcsine laws 

      Swanepoel, Jan W.H. (SASA, 2017)
      Firstly, we provide simple elementary proofs to derive the exact distributions of the areas under functions of a Brownian motion process and a Brownian bridge process. In the latter case, a solution is therefore provided ...