Abstract
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter H ∈ ] 1 4 , 1 2 [ given by Coutin and Qian in [Probab. Theory Related Fields 122 (2002) 108–140], we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Annales de l'Institut Henri Poincare / Probabilites et statistiques
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.