BibTex format
@unpublished{Li:2021,
author = {Li, X-M and Gehringer, J},
publisher = {ArXiv},
title = {Functional limit theorems for the fractional Ornstein-Uhlenbeck process},
url = {https://arxiv.org/abs/2006.11540},
year = {2021}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the joint convergence to a limit with both Gaussian and non-Gaussian components. This is valid for any L2 functions, whereas for functions with stronger integrability properties the convergence is shown to hold in the Hölder topology. As an application we prove a `rough creation' result, i.e. the weak convergence of a family of random smooth curves to a non-Markovian random process with rough sample paths. This includes the second order problem and the kinetic fractional Brownian motion model.
AU - Li,X-M
AU - Gehringer,J
PB - ArXiv
PY - 2021///
TI - Functional limit theorems for the fractional Ornstein-Uhlenbeck process
UR - https://arxiv.org/abs/2006.11540
UR - http://hdl.handle.net/10044/1/92640
ER -