Abstract
The central limit theorem for nonhomogeneous processes with independent increments with semi-Markov switchings with a uniformly ergodic imbedded Markov chain is proved.
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Literature cited
V. S. Korolyuk and V. V. Korolyuk, “The central limit theorem for homogeneous processes with independent increments and semi-Markov switchings,” Ukr. Mat. Zh.,35, No. 6, 760–763 (1983).
V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).
M. G. Krein, “Integral equations on a halfline with a kernel depending on the difference of arguments,” Usp. Mat. Nauk,18, No. 5, 3–120 (1958).
V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of Phase Amalgamation of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).
V. V. Korolyuk, “Stochastic systems with semi-Markov switching,” Preprint No. 35, Institute of Cybernetics, Academy of Sciences of the Ukrainian SSR, Kiev (1983).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 134–137, January, 1991.
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Korolyuk, V.V. Central limit theorem for nonhomogeneous processes with independent increments with semi-Markov switchings. Ukr Math J 43, 111–114 (1991). https://doi.org/10.1007/BF01066916
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DOI: https://doi.org/10.1007/BF01066916