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Moments of First-Passage Places for Jump-Diffusion Processes

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  • Mario Lefebvre

    (Polytechnique Montréal)

Abstract

Let T be the first time that the time-homogeneous jump-diffusion process X(t) leaves the interval (a, b). The jump size is assumed to be a positive constant. We derive exact formulas for E[Xk(T)] in special cases. For the general case, an approximate analytical expression can be obtained for E[Xk(T)]. This expression is precise when the jump size is small.

Suggested Citation

  • Mario Lefebvre, 2021. "Moments of First-Passage Places for Jump-Diffusion Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 245-253, February.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00181-4
    DOI: 10.1007/s13171-019-00181-4
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    References listed on IDEAS

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    1. Mario Abundo, 2010. "On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 473-490, September.
    2. Lefebvre, Mario, 1997. "First hitting place distributions for the Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 309-312, June.
    3. Lefebvre, Mario, 1989. "Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 281-287, August.
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