A note on stochastic integrals as $L^2$-curves

Abstract

In a work of van Gaans (2005a) stochastic integrals are regarded as $L^2$-curves. In Filipović and Tappe (2008) we have shown the connection to the usual Itô-integral for càdlàg-integrands. The goal of this note is to complete this result and to provide the full connection to the Itô-integral. We also sketch an application to stochastic partial differential equations.

6 pages

References in corpus (1)

• Existence of Lévy term structure models

Cited by in corpus (2)

• Isomorphisms for spaces of predictable processes and an extension of the Itô integral
• The Itô integral with respect to an infinite dimensional Lévy process: A series approach