Browsing Faculty of Natural and Agricultural Sciences by Subject "Vector lattice"

Now showing items 1-8 of 8

    • 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 ...

    • 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 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 ...

    • 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 ...

    • 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, ...

    • Vector lattices and f-algebras: the classical inequalities 

      Buskes, G.; Schwanke, C. (Duke Univ Press, 2018)
      We present some of the classical inequalities in analysis in the context of Archimedean (real or complex) vector lattices and f-algebras. In particular, we prove an identity for sesquilinear maps from the Cartesian square ...