Now showing items 1-8 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 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 ...
• #### 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 p-inequality 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, 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, ...
• #### Vector lattices and f-algebras: 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 f-algebras. In particular, we prove an identity for sesquilinear maps from the Cartesian square ...

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