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ISSN 1547-7363(online) ISSN 0094-9000(print)
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
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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
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