Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615483 | Journal of Mathematical Analysis and Applications | 2015 | 14 Pages |
Abstract
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 in the classical setting which yields a local martingale. 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 extended Itô integral is a special case of the constructed integral in the vector lattice.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jacobus J. Grobler, Coenraad C.A. Labuschagne,