Issoglio, E and Riedle, M (2014) Cylindrical fractional Brownian motion in Banach spaces. Stochastic Processes and their Applications, 124 (11). pp. 3507-3534. ISSN 0304-4149
Abstract
In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Loève expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsevier B.V. This is an author produced version of a paper published in Stochastic Processes and their Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Cylindrical fractional Brownian motion; Stochastic integration in Banach spaces; Stochastic partial differential equations; Fractional Ornstein–Uhlenbeck process; γ-radonifying; Cylindrical measures |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 May 2016 14:17 |
Last Modified: | 17 Jan 2018 18:01 |
Published Version: | http://dx.doi.org/10.1016/j.spa.2014.05.010 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.spa.2014.05.010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98922 |