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Joint distributions of the the infimum, supremum, and end of a Brownian motion with jumps

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In this paper, we compute the joint distributions of the infimum, supremumm, and end of a Brownian motion with jumps. The final time of a Brownian motion with jumps is taken at an exponentially distributed random moment independent of the process. This corresponds to the Laplace transform with respect to the deterministic time of the considered joint distributions.

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References

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg State University, St. Petersburg, Russia

    A. N. Borodin

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  1. A. N. Borodin
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Correspondence to A. N. Borodin.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 396, 2011, pp. 73−87.

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Borodin, A.N. Joint distributions of the the infimum, supremum, and end of a Brownian motion with jumps. J Math Sci 188, 677–685 (2013). https://doi.org/10.1007/s10958-013-1157-4

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  • DOI: https://doi.org/10.1007/s10958-013-1157-4

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