The Itô integral for Brownian motion in vector lattices. Part1
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Grobler, Jacobus J.
Labuschagne, Coenraad C.A.
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Elsevier
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Abstract
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 construction does not depend on a probability measure space. The classical case of the Itô integral is a special case of the constructed integral in the vector lattice
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Grobler, J.J. & Labuschagne, C.C.A. 2015. The Itô integral for Brownian motion in vector lattices. Part1. Journal of mathematical analysis and applications, 423(1):797-819. [https://doi.org/10.1016/j.jmaa.2014.08.013]