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A Limit Theorem for Regime-Switching Diffusion Processes

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An approximation of a regime-switching diffusion process by a family of regime-switching jump Markov processes is considered. The corresponding limit theorem is proved.

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References

  1. M. Freidlin, Functional Integration and Partial Differential Equations, Princeton Univ. Press, Princeton, New Jersey (1985).

  2. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, Naukova Dumka, Kiev (1968).

  3. R. Z. Khasminskii, “Stability of regime-switching stochastic differential equations,” Probl. Peredachi Inf., 48, No. 3, 70–82 (2012).

    MathSciNet  MATH  Google Scholar 

  4. G. Yin and C. Zhu, Hybrid Switching Diffusions, Springer, New York (2010).

    Book  MATH  Google Scholar 

  5. Shao-Qin Zhang, “Regime-switching diffusion processes: strong solutions and strong Feller property,” Stoch. Anal. Appl., 38, No. 1, 97–123 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Kato, Perturbation Theory of Linear Operators [in Russian], Mir, Moscow (1972).

    Google Scholar 

  7. A. Friedman, Stochastic Differential Equations and Applications, Academic Press, New York (1975).

    MATH  Google Scholar 

  8. I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Stochastic Processes, Nauka, Moscow (1977).

    MATH  Google Scholar 

  9. A. N. Borodin, “Distributions of functionals of switching diffusions with jumps,” Zap. Nauchn. Semin. POMI, 474, 28–45 (2018).

    Google Scholar 

  10. A. N. Borodin, “Joint distributions of functionals of telegraph process and switching diffusions,” Zap. Nauchn. Semin. POMI, 466, 38–53 (2017).

    Google Scholar 

  11. A. N. Borodin, “Limit behaviour of a compound Poisson process with switching between multiple values,” Zap. Nauchn. Semin. POMI, 486, 44–62 (2019).

    Google Scholar 

  12. X. Mao and C. Yuan, Stohastic Differential Equations with Markovian Switching, Imperial College Press, London (2006).

    Book  Google Scholar 

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Correspondence to N. V. Smorodina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 267–276.

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Smorodina, N.V., Faddeev, M.M. A Limit Theorem for Regime-Switching Diffusion Processes. J Math Sci 268, 704–710 (2022). https://doi.org/10.1007/s10958-022-06240-w

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  • DOI: https://doi.org/10.1007/s10958-022-06240-w

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