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On the local times of fractional Ornstein-Uhlenbeck process. (English) Zbl 1102.60035

Summary: We study the local times of the fractional Ornstein-Uhlenbeck process X H with Hurst index 1/2<H<1 solving the Langevin equation with fractional noise

dX t H =-X t H dt+νdB t H ,X 0 H =x,

where ν>0 and B H is a fractional Brownian motion with Hurst index 1/2, H<1. We give the Tanaka formula for the process and some properties of local times.

60G15Gaussian processes
60J55Local time, additive functionals
60H05Stochastic integrals
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