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Theory of Probability and Mathematical Statistics

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Properties of the stochastic ordering for discrete distributions and their applications to the renewal sequence generated by a nonhomogeneous Markov chain


Author: V. V. Golomozyĭ
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 33-43
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/tpms/1046
Published electronically: February 21, 2019
MathSciNet review: 3745997
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Abstract: The generalized stochastic ordering is studied for which the dominating sequence is not necessarily a probability distribution so that its total mass may exceed unity. We study the stochastic ordering for sums as well as random sums of independent as well as dependent random variables. A stochastic ordering is constructed for the renewal sequence generated by a nonhomogeneous Markov chain. The consideration is restricted to the case of discrete random variables.


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Additional Information

V. V. Golomozyĭ
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: mailtower@gmail.com

DOI: https://doi.org/10.1090/tpms/1046
Keywords: Discrete Markov chain, stability of distributions, coupling method, theory of coupling
Received by editor(s): September 27, 2017
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society