The Itô integral for Brownian motion in vector lattices: Part 2 |
| |
Authors: | Jacobus J Grobler Coenraad CA Labuschagne |
| |
Institution: | 1. Unit for Business Mathematics and Informatics, North-West University, Potchefstroom Campus, Potchefstroom 2520, South Africa;2. Department of Finance and Investment Management, University of Johannesburg, PO Box 524, Aucklandpark 2006, Johannesburg, South Africa |
| |
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. |
| |
Keywords: | Bochner integral Brownian motion Conditional expectation Itô integral Martingale Vector lattice |
本文献已被 ScienceDirect 等数据库收录! |
|