Fluctuations of an asymptotically dissipative process with Markov switching

Kinash  Anastasia Volodymyrivna

Kinash Anastasia Volodymyrivna ¹

¹ National University "Lviv Polytechnic", Lviv , 79000, Ukraine

Keywords: fluctuations, asymptotically dissipative process, Markov switching

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Abstract

In the article we conside fluctuations of an asymptotic dissipative process with Markov switching in the diffusion approximation scheme under balance conditions on singular perturbation by a small series parameter. The balance condition is crucial for obtaining of a limiting generator in the solution of the singular perturbation problem. Sufficient conditions for the dissipativity of obtaining of limiting diffusion process are formulated in terms of Lyapunov function of the system. The Lyapunov function is averaged over the stationary distribution of Markov switching process. The limited generator of system fluctuations was obtained.

References

[1] Khasminsky R.Z. Stability of systems of differential equations at random perturbations of their parameters // Moscow: “Nauka 1969. 368 p.

[2] A. Mazurov and P. Pakshin Stochastic dissipativity with risk-sensitive storage function and related control problems // ICIC Express Letters - 2008. - 3 , N1. - P. 53-60.

[3] Samoilenko A.M., Stanzhytskyi O.M. Qualitative and asymptotic analysis of differential equations with random perturbations: Monograph // K. Naukova Dumka - 2009. - 336 p.

[4] B. Brogliato Dissipative Systems Analysis and Control // Springer - 2005. - 585 p.

[5] V. Koroliuk and N. Limnious Stochastic Systems in Merging Phase Space. // World Scientific Publishing - 2005.

[6] Y. M. Chabaniuk and V. Koroliuk and N. Limnios Fluctuation of stochastic systems with average equilibrium point // C. R. Acad. Sci. - 2007. - 1 , N345. - P. 405-410.

[7] A.V. Kinash, Y.M. Chabanyuk, U.T. Khimka Asymptotic dissipativity of a diffusion process // Mathematical and computer modeling. Series: Physical and mathematical sciences. Kamianets-Podilskyi. - 2014. - N11. - P. 77-87.

[8] Chabaniuk Y.M. Asymptotic normality of the jump procedure of stochastic approximation in the Markov environment // Scientific Bulletin of Chernivtsi Univ. Mathematics. Chernivtsi. - 2007. - N 349. - P. 128-133.

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ACS Style: Kinash , A.V. Fluctuations of an asymptotically dissipative process with Markov switching. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Kinash AV. Fluctuations of an asymptotically dissipative process with Markov switching. Bukovinian Mathematical Journal. 2016; 3(2).
Chicago/Turabian Style: Anastasia Volodymyrivna Kinash . 2016. "Fluctuations of an asymptotically dissipative process with Markov switching". Bukovinian Mathematical Journal. 3 no. 2.

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