Asymptotic dissipativity of the diffusion process in the asymptotic small diffusion scheme

• Autorzy: Kinash A. , Chabanyuk Y. , Khimka U.

Identyfikatory

DOI

10.17512/jamcm.2015.4.09

• Języki publikacji: EN

Abstrakty

EN

This paper considers the random evolution with Markov switching. The resulting limited process is diffusion and depends on the small series parameter. The sufficient conditions of dissipativity of the limited process were obtained. Since the conditions of the Model Limit theorem and dissipativity conditions were set asymptotic dissipativity of the output process.

Słowa kluczowe

EN

small series parameter; diffusion; asymptotic dissipativity

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 93--103
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kinash A.

• National University Lviv Polytechnic, Lviv, Ukraine

autor

Chabanyuk Y.

• Lublin University of Technology, Lublin, Poland

autor

Khimka U.

• National University Lviv Polytechnic, Lviv, Ukraine

Bibliografia

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• [3] Zhernovyi Yu., Kopytko B., Zhernovyi K., The busy period for the M /G/1/m θ system with service time dependent of the queue length, Journal of Applied Mathematics and Computational Mechanics 2013, 12(4), 127-133.
• [4] Kiikovska O.I., Chabanyuk Ya.M., Random evolution in the asymptotically small diffusion scheme with Markov switching, Cybernetics and Systems Analysis 2013, 49, 2, 164-169 (in Ukrainian).
• [5] Khasminskii R.Z., Stability of Systems of Differential Equations with Random Perturbations of Their Parameters, Nauka, Moscow 1969, 368 (in Russian).
• [6] Khasminskii R.Z., About dissipativity of random processes defined by differential equations, Probl. peredachu infor. 1965, 1, 1, 88-104 (in Russian).
• [7] Samoilenko A.M., Stangytckyi O.M., Qualitative and asymptotic analysis of differential equations with random perturbations, Naukova dumka 2009, 336 (in Ukrainian).
• [8] Kinash A.V., Chabanyuk Ya.M., Khimka U.T., Asymptotic dissipativity of diffusion process, Mathematical and Computer Modeling, Series: Physical and Mathematical Sciences 2014, 11, 78-87 (in Ukrainian).