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• W3036402524 abstract "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 $L^2$ functions, whereas for functions with stronger integrability properties the convergence is shown to hold in the Holder 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." @default.
• W3036402524 created "2020-06-25" @default.
• W3036402524 creator A5056219161 @default.
• W3036402524 creator A5064478014 @default.
• W3036402524 date "2020-06-20" @default.
• W3036402524 modified "2023-09-25" @default.
• W3036402524 title "Functional limit theorems for the fractional Ornstein-Uhlenbeck process" @default.
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• W3036402524 doi "https://doi.org/10.48550/arxiv.2006.11540" @default.
• W3036402524 hasPublicationYear "2020" @default.
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