Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611-8105, USA
Copyright © 2010 J. K. Brooks and J. T. Kozinski. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish the existence of a stochastic integral in a nuclear space setting
as follows. Let , , and be nuclear spaces which satisfy the following
conditions: the spaces are reflexive, complete, bornological spaces such that their
strong duals also satisfy these conditions. Assume that there is a continuous
bilinear mapping of into . If is an integrable, -valued predictable
process and is an -valued square integrable martingale, then there exists a
-valued process called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.