Abstract
In this chapter, we study the relative compactness of semi-Markov random evolutions in the diffusion approximation under the balance condition. The behavior of semi-Markov random evolutions is studied on the time interval [0, t / ε 2] for all t ∈ [0, T] and ε > 0. In our investigation, we use the criteria of relative compactness for the processes with values in a separable Banach space (Section 5.1) and the martingale methods.
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© 1995 Springer Science+Business Media Dordrecht
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Korolyuk, V., Swishchuk, A. (1995). Compactness of Semi-Markov Random Evolutions in the Diffusion Approximation. In: Semi-Markov Random Evolutions. Mathematics and Its Applications, vol 308. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1010-5_8
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DOI: https://doi.org/10.1007/978-94-011-1010-5_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4439-4
Online ISBN: 978-94-011-1010-5
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