Browsing Research Output by Subject "Vector lattice"
Now showing items 18 of 8

Girsanov’s theorem in vector lattices
(Springer, 2019)In this paper we formulate and proof Girsanov’s theorem in vector lattices. To reach this goal, we develop the theory of crossvariation processes, derive the crossvariation formula and the Kunita–Watanabe inequality. ... 
The Itô integral for Brownian motion in vector lattices. Part 2
(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
(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
(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 pinequality for continuous time ... 
The Kolmogorov–Čentsov theorem and Brownian motion in vector lattices
(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
(Elsevier, 2017)We define and study order continuity, topological continuity, γHöldercontinuity and Kolmogorov–Čentsovcontinuity of continuoustime stochastic processes in vector lattices and show that every such kind of continuous ... 
Quadratic variation of martingales in Riesz spaces
(Elsevier, 2014)We derive quadratic variation inequalities for discretetime martingales, sub and supermartingales in the measurefree setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, ... 
Vector lattices and falgebras: the classical inequalities
(Duke Univ Press, 2018)We present some of the classical inequalities in analysis in the context of Archimedean (real or complex) vector lattices and falgebras. In particular, we prove an identity for sesquilinear maps from the Cartesian square ...