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2 Journal of Applied Mathematics and Computational Mechanics

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The limit properties diffusion process in a semi-Markov environment

Chabanyuk Y., Rosa W.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 1

5--14

In this paper we consider the stochastic diffusion process with semi-Markov switchings in an averaging scheme. We present results and conditions on convergence to the classic diffusion process, in case with semi-Markov process perturbation is uniformly ergodic. We used small parameter scheme to get the main result.

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

Kinash A., Chabanyuk Y., Khimka U.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 4

93--103

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.