Theory of Probability and Mathematical Statistics
Transfer principle for fractional Ornstein–Uhlenbeck processes
Tommi Sottinen and Lauri Viitasaari
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Abstract: We prove the transfer principle for fractional Ornstein–Uhlenbeck processes, i.e., we construct a Brownian motion that has the same filtration as the fractional Ornstein–Uhlenbeck process and then represent the fractional Ornstein–Uhlenbeck process by using the constructed Brownian motion. As applications of the transfer principle, we consider data-driven prediction by providing both prediction laws and consistent parameter estimation.
Keywords: Fractional Brownian motion, fractional Ornstein–Uhlenbeck process, Langevin equation, transfer principle, prediction
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