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n-Dimensional Laplace Transforms of Occupation Times for Pre-Exit Diffusion Processes

Author

Listed:
  • Yingchun Deng

    (Hunan Normal University)

  • Xuan Huang

    (Hunan Normal University)

  • Ya Huang

    (Hunan Normal University)

  • Xuyan Xiang

    (Hunan University of Arts and Science
    Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone)

  • Jieming Zhou

    (Hunan Normal University)

Abstract

In this paper, we adopt a Poisson approach to find Laplace transforms of joint occupation times over n disjoint intervals for pre-exit diffusion processes. Then we generalize previous result for the 2-dimensional case and the 3-dimensional case.

Suggested Citation

  • Yingchun Deng & Xuan Huang & Ya Huang & Xuyan Xiang & Jieming Zhou, 2020. "n-Dimensional Laplace Transforms of Occupation Times for Pre-Exit Diffusion Processes," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 345-360, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0404-x
    DOI: 10.1007/s13226-020-0404-x
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    References listed on IDEAS

    as
    1. Landriault, David & Shi, Tianxiang, 2015. "Occupation times in the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 75-82.
    2. Li, Yingqiu & Zhou, Xiaowen, 2014. "On pre-exit joint occupation times for spectrally negative Lévy processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 48-55.
    3. Jin, Can & Li, Shuanming & Wu, Xueyuan, 2016. "On the occupation times in a delayed Sparre Andersen risk model with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 304-316.
    4. A. E. Kyprianou & J. C. Pardo & J. L. Pérez, 2014. "Occupation Times of Refracted Lévy Processes," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1292-1315, December.
    5. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    6. Ning Cai & Nan Chen & Xiangwei Wan, 2010. "Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 412-437, May.
    7. Xuebing Kuang & Xiaowen Zhou, 2017. "n -Dimensional Laplace Transforms of Occupation Times for Spectrally Negative Lévy Processes," Risks, MDPI, vol. 5(1), pages 1-14, January.
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    Cited by:

    1. Xuan Huang & Jieming Zhou, 2022. "General Draw-Down Times for Refracted Spectrally Negative Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 875-891, June.

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