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On The Local Times of Fractional Ornstein–Uhlenbeck Process

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Abstract

In this short note, 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

$$ \hbox{d}X_{t}^{H} = -X_{t}^{H} \hbox{d}t + \nu \hbox{d}B_{t}^{H}, \quad X_{0}^{H} = x, $$

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

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Donghua University, 1882 West Yan’an Rd., Shanghai, 200051, P.R. China

    Litan Yan & Ming Tian

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  1. Litan Yan
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  2. Ming Tian
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Correspondence to Litan Yan.

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Mathematics Subject Classifications (2000): 60G15, 60J55, 60H05. *The Project-sponsored by SRF for ROCS, SEM.

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Yan, L., Tian, M. On The Local Times of Fractional Ornstein–Uhlenbeck Process. Lett Math Phys 73, 209–220 (2005). https://doi.org/10.1007/s11005-005-0018-6

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  • DOI: https://doi.org/10.1007/s11005-005-0018-6

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