Browsing Faculty of Natural and Agricultural Sciences by Subject "Brownian motion"
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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 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 ... -
A note on Brownian areas and arcsine laws
(SASA, 2017)Firstly, we provide simple elementary proofs to derive the exact distributions of the areas under functions of a Brownian motion process and a Brownian bridge process. In the latter case, a solution is therefore provided ...