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On explicit occupation time distributions for Brownian processes


  • Hooghiemstra, Gerard


Explicit expressions for the occupation time distribution of Brownian bridge, excursion and meander are derived using Kac's formula and results of Durrett et al. (Ann. Probab. 5 (1977) 117). The first two distributions appeared in Takács (Meth. Comput. Appl. Probab. 1 (1999) 7), and were derived using weak convergence of simple random walk.

Suggested Citation

  • Hooghiemstra, Gerard, 2002. "On explicit occupation time distributions for Brownian processes," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 405-417, February.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:4:p:405-417

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    References listed on IDEAS

    1. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    2. Kalashnikov, Vladimir & Konstantinides, Dimitrios, 2000. "Ruin under interest force and subexponential claims: a simple treatment," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 145-149, August.
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    Cited by:

    1. Makarov, R. & Metzler, A. & Ni, Z., 2015. "Modelling default risk with occupation times," Finance Research Letters, Elsevier, vol. 13(C), pages 54-65.
    2. Chi, Zhiyi & Pozdnyakov, Vladimir & Yan, Jun, 2015. "On expected occupation time of Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 83-87.


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