Weak convergence of the family of semi-Markov processes to the diffusion process
1 Department of Mathematical Problems of Management and Cybernetics, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords:
semi-Markov processes
Abstract
Sufficient соndition of weak convergence of the family of semi-Markov processes to a diffusion process іп the series with a small parameter $ε > 0, ε → 0$ іn terms of local characteristics of the semi-Markov process are formulated.
References
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[3] Samoilenko I.B., Malik I.B. Convergence of a semi-Markovian and accompanying Markov process to a Markov process // UMZh. 2010, Vol. 62, № 5, p. 674-681.
[4] Sviridenko M.N. About conditions of convergence of a family of semi-Markov processes to a Markov process. - M.: Preprint of MYTISHCHI. - 1986. - 17 p.
[5] Sviridenko M.N. Martingale characterization of limit distributions in the space of functions without discontinuities of second kind // Math. Notes. - 1998.- 43, No 5. - P. 398-402 .
Cite
- ACS Style
- Malyk, I. Weak convergence of the family of semi-Markov processes to the diffusion process. Bukovinian Mathematical Journal. 2018, 2
- AMA Style
- Malyk I. Weak convergence of the family of semi-Markov processes to the diffusion process. Bukovinian Mathematical Journal. 2018; 2(1).
- Chicago/Turabian Style
- Igor Malyk. 2018. "Weak convergence of the family of semi-Markov processes to the diffusion process". Bukovinian Mathematical Journal. 2 no. 1.
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