Browsing by Subject "Riesz space"

Now showing items 1-4 of 4

    • 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, ...

    • Vektorintegrasie met toepassings op stogastiese prosesse in Riesz ruimtes 

      Zeelie, Jacobus (North-West University (South Africa), Potchefstroom Campus, 2016)
      Daar is al 'n verskeidenheid van teorieë ontwikkel om die abstrakte Lebesgue integraal te veralgemeen vir funksies of mate wat vektorwaardig is. Ons bestudeer drie van die mees suksesvolle integrasie teorieë, die van ...