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Letters in Mathematical Physics

, Volume 73, Issue 3, pp 209–220 | Cite as

On The Local Times of Fractional Ornstein–Uhlenbeck Process

  • Litan Yan
  • Ming Tian
Article

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.

Keywords

fractional Brownian motion the fractional Itô integrals Itô type formula Malliavin derivative the fractional Ornstein–Uhlenbeck process Lamperti transform and local times 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceDonghua UniversityShanghaiP.R. China

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