Abstract
One presents the results obtained recently by the collaborators of the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, regarding limit theorems for additive functionals of Markov and semi-Markov processes. One makes use of the theory of inversion of singularly perturbed semigroups of operators in the phase extension scheme and of the methods of asymptotic analysis of singularly perturbed Markov renewal equations.
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Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 229–246, 1986.
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Korolyuk, V.S. The central limit theorem for additive functionals of Markov and semi-Markov processes. J Math Sci 38, 2299–2308 (1987). https://doi.org/10.1007/BF01093831
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DOI: https://doi.org/10.1007/BF01093831