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Double Merging of the Phase Space for Stochastic Differential Equations with Small Additions in Poisson Approximation Conditions

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Abstract

Double merging of phase space for the stochastic evolutionary system is performed. The case is considered where system’s perturbations are determined by the impulse process at the Poisson approximation scheme. The limiting process under such conditions has two components: deterministic shift and Poisson jump addition.

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References

  1. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and their Applications [in Russian], Naukova Dumka, Kyiv (1976).

  2. V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Dordrecht, Kluwer (1999).

  3. V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, Singapore (2005).

  4. V. S. Korolyuk, N. Limnios, and I. V. Samoilenko, “Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach,” Comptes Rendus Mathématique, Vol. 354, Iss. 7, 723–728 (2016).

  5. I. V. Samoilenko and A. V. Nikitin, “Differential equations with small stochastic terms under the Lévy approximation conditions,” Ukr. Math. J., Vol. 69, No. 9, 1445–1454 (2018).

  6. A. M. Samoilenko and O. M. Stanzhytskyi, Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations, World Scientific, Singapore (2011).

  7. V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in System Reliability Problems [in Russian], Naukova Dumka, Kyiv (1982).

  8. I. V. Samoilenko, Y. M. Chabanyuk, A. V. Nikitin, and U. T. Khimka, “Differential equations with small stochastic additions under Poisson approximation conditions,” Cybern. Syst. Analysis, Vol. 53, No. 3, 410–416 (2017).

  9. I. V. Samoilenko, Y. M. Chabanyuk, and A. V. Nikitin, “Asymptotic dissipativity of random processes with impulse perturbation in the Poisson approximation scheme,” Cybern. Syst. Analysis, Vol. 54, No. 2, 205–211 (2018).

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Correspondence to I. V. Samoilenko.

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2019, pp. 108–116

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Samoilenko, I.V., Nikitin, A.V. Double Merging of the Phase Space for Stochastic Differential Equations with Small Additions in Poisson Approximation Conditions. Cybern Syst Anal 55, 265–273 (2019). https://doi.org/10.1007/s10559-019-00131-w

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  • DOI: https://doi.org/10.1007/s10559-019-00131-w

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