Abstract
We prove a limit theorem on the approximation of point mixing processes subject to rarefaction by general renewal processes. This theorem contains a weaker condition on the mixing coefficient than the known conditions.
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V. A. Gasanenko, “Processes subject to rarefaction,” Ukr. Mat. Zh., 35, No. 1, 27–30 (1983).
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
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V. V. Anisimov, Random Processes with Discrete Component. Limit Theorems [in Russian], Kiev, Vyshcha Shkola (1988).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 471–475, April, 1998.
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Gasanenko, V.O. A limit theorem for mixing processes subject to rarefaction. I. Ukr Math J 50, 533–538 (1998). https://doi.org/10.1007/BF02487385
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DOI: https://doi.org/10.1007/BF02487385