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On expected occupation time of Brownian bridge


  • Chi, Zhiyi
  • Pozdnyakov, Vladimir
  • Yan, Jun


Consider a Brownian bridge from 0 to c>0. It is known that the density of the expected occupation time by the Brownian bridge is constant in [0,c]. We give a simple elementary proof for this result based on a direct examination of the corresponding integral. The expected occupation time plays an important role in the analysis of animal movement.

Suggested Citation

  • Chi, Zhiyi & Pozdnyakov, Vladimir & Yan, Jun, 2015. "On expected occupation time of Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 83-87.
  • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:83-87 DOI: 10.1016/j.spl.2014.11.009

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    References listed on IDEAS

    1. Howard, Peter & Zumbrun, Kevin, 1999. "Shift invariance of the occupation time of the Brownian bridge process," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 379-382, December.
    2. Hooghiemstra, Gerard, 2002. "On explicit occupation time distributions for Brownian processes," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 405-417, February.
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