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Journal of Mathematical Sciences

, Volume 244, Issue 5, pp 733–742 | Cite as

Limit Behavior of a Compound Poisson Process with Switching

  • A. N. BorodinEmail author
Article
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The paper deals with the limit behavior of a compound Poisson process with switching. The switching is provided by Bernoulli’s random variables. Under a suitable normalization, the limit process is a Brownian motion with switching variance.

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References

  1. 1.
    A. N. Borodin, Stochastic Processes, Birkhäuser, Cham (2017).CrossRefGoogle Scholar
  2. 2.
    A. N. Borodin, “On joint distributions of functionals of the telegraph process and switching diffusions,” Zap. Nauchn. Semin. POMI, 466, 38–53 (2017).Google Scholar
  3. 3.
    P. Billingsley, Convergence of Probability Measures, John Wiley & Sons Inc., New York, London, Sydney, Toronto (1968).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. Petersburg State UniversitySt. PetersburgRussia

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