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The local time of the Markov processes of Ornstein–Uhlenbeck type

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  • Tong, Changqing
  • Lin, Zhengyan
  • Zheng, Jing

Abstract

We prove the existence of the local time of the Ornstein–Uhlenbeck type process X={Xt,t∈R+} driven by a general Lévy process. The conditions of the continuity in time variable t and the regularity property of the local time are given, under mild regularity conditions on the driving Lévy process. These results give information about the local properties of sample functions of the process.

Suggested Citation

  • Tong, Changqing & Lin, Zhengyan & Zheng, Jing, 2012. "The local time of the Markov processes of Ornstein–Uhlenbeck type," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1229-1234.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1229-1234
    DOI: 10.1016/j.spl.2012.03.003
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    References listed on IDEAS

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    1. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    2. Imkeller, P. & Pavlyukevich, I., 2006. "First exit times of SDEs driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 611-642, April.
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