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Distributions of the location of maximuma and minimuma for diffusions with jumps

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The paper deals with methods of computation of distributions of location for maxima and minima for diffusions with jumps. As an example, we obtain explicit formulas for distributions of location for the maximum of the process which is equal to the sum of a Brownian motion and the compound Poisson process. Bibliography: 8 titles.

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References

  1. E. Csáki, A. Földes, and P. Salminen, "On the joint distribution of the maximum and its location for a linear diffusion," Ann. Inst. H. Poinaré, 23, 179–194 (1987).

    MATH  Google Scholar 

  2. A. N. Borodin, "Distribution of functionals of diffusions with jumps," Zap. Nauchn. Semin. POMI, 339, 15–36 (2006).

    MATH  Google Scholar 

  3. A. N. Borodin, "Distribution of functionals of the bridges of diffusions with jumps," Zap. Nauchn. Semin. POMI, 341, 34–47 (2007).

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  4. A. N. Borodin, "On the first exit time from an interval for diffusions with jumps," Zap. Nauchn. Semin. POMI, 364, 70–88 (2009).

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  5. E. Mordecki, "Ruin probabilities for Lévy processes with mixed exponential negative jumps," Teor. Veroyatn. Primen., 48, 188–194 (2003).

    MathSciNet  Google Scholar 

  6. A. V. Skorohod, Processes With Independent Increments [in Russian], Moscow (1964).

  7. A. N. Borodin, "Distribution of functionals of some processes with independent increments," Vestn. St. Peter. Univ., 4, 7–20 (2005).

    Google Scholar 

  8. A. N. Borodin and P. Salminen, Handbook of Brownian Motion-Fats and Formulae, 2nd ed., Birkhäuser, Basel-Boston-Berlin (2002).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute, 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. 368, 2009, pp. 75–94.

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Borodin, A.N. Distributions of the location of maximuma and minimuma for diffusions with jumps. J Math Sci 167, 474–485 (2010). https://doi.org/10.1007/s10958-010-9933-x

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  • DOI: https://doi.org/10.1007/s10958-010-9933-x

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