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Journal of Mathematical Sciences

, Volume 167, Issue 4, pp 474–485 | Cite as

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

  • A. N. Borodin
Article
  • 18 Downloads

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.

Keywords

Russia Brownian Motion Poisson Process Explicit Formula Mathematical Institute 
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References

  1. 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).zbMATHGoogle Scholar
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    A. N. Borodin, "Distribution of functionals of diffusions with jumps," Zap. Nauchn. Semin. POMI, 339, 15–36 (2006).zbMATHGoogle Scholar
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    A. N. Borodin, "Distribution of functionals of the bridges of diffusions with jumps," Zap. Nauchn. Semin. POMI, 341, 34–47 (2007).zbMATHMathSciNetGoogle Scholar
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    A. N. Borodin, "On the first exit time from an interval for diffusions with jumps," Zap. Nauchn. Semin. POMI, 364, 70–88 (2009).Google Scholar
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    E. Mordecki, "Ruin probabilities for Lévy processes with mixed exponential negative jumps," Teor. Veroyatn. Primen., 48, 188–194 (2003).MathSciNetGoogle Scholar
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    A. V. Skorohod, Processes With Independent Increments [in Russian], Moscow (1964).Google Scholar
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    A. N. Borodin, "Distribution of functionals of some processes with independent increments," Vestn. St. Peter. Univ., 4, 7–20 (2005).Google Scholar
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    A. N. Borodin and P. Salminen, Handbook of Brownian Motion-Fats and Formulae, 2nd ed., Birkhäuser, Basel-Boston-Berlin (2002).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical InstituteSt. PetersburgRussia

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