Browsing Research Output by Subject "Martingale"
Now showing items 1-5 of 5
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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 cross-variation processes, derive the cross-variation 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 ... -
The quadratic variation of continuous time stochastic processes in vector lattices
(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
(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, ...