Now showing items 1-5 of 5

• #### 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 ...

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