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Theory of Probability and Mathematical Statistics

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A bound for the remainder term in the asymptotic expansion of a functional constructed from a semi-Markov random evolution


Authors: V. S. Koroliuk and I. V. Samoilenko
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 217-227
MSC (2010): Primary 60J25; Secondary 35C20
DOI: https://doi.org/10.1090/tpms/1072
Published electronically: August 19, 2019
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Abstract: The regular as well as singular component of the asymptotic expansion of a functional constructed from a semi-Markov random evolution is found, and regularity of the initial data is shown in Theory Probab. Math. Statist. 96 (2018), 83-100. A bound for the remainder term of the asymptotic expansion obtained in the above-mentioned paper is studied in the current paper.


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Additional Information

V. S. Koroliuk
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv, Ukraine 01601
Email: vskorol@yahoo.com

I. V. Samoilenko
Affiliation: Faculty of Computer Science and Cybernetics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: isamoil@i.ua

DOI: https://doi.org/10.1090/tpms/1072
Keywords: Asymptotic expansion, semi-Markov process, random evolution, remainder term
Received by editor(s): February 16, 2018
Published electronically: August 19, 2019
Additional Notes: This paper as well as its first part \cite{KoSam} contains results obtained under the support given by the Presidential Grant 0117U007015 from the State Fund of Fundamental Researches of Ukraine
Article copyright: © Copyright 2019 American Mathematical Society