Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Properties of a stochastic dominant for discrete distributions and its application for a renewal sequence generated by time-inhomogeneous Markov chain
V. V. Golomoziy
Abstract: Generalized stochastic dominance when dominating sequence is not neccessary a probability distribution and may have total mass bigger than one is considered in this paper. Dominance of sums of random variables, random sums for both independent and depenedent random variables are investigated. Dominating sequnce for a renewal sequence generated by time-inhomogeneous Markov chain was obtained. Only discrette random variables are considered.
Keywords: Discrete Markov chains, stability of distributions, coupling method, coupling theory
1. S. P. Mayn, R. L. Tweedie, Markov chains and stochastic Stability, Springer-Verlag, 1993.
2. H. Thorisson, Coupling, stationarity, and regeneration, Springer, New York, 2000.
3. T. Lindvall, Lectures on the coupling method, John Wiley and Sons, 1991.
4. V. Golomoziy, M. Kartashov, On the integrability of the coupling moment for time-inhomoge-neous Markov chains, Theory Probab. Math. Statist., 89 (2014), 1-12.
5. V. Golomoziy, An estimate of the expectation of the excess of a renewal sequence generated by a time-inhomogeneous Markov chain if a square-integrable majorizing sequence exists, Theory Probab. Math. Statist., 94 (2017), 53-62.
6. V. Golomoziy, An estimate for an expectation of the simultaneous renewal for time-inhomoge- neous Markov chains, Mod. Stoch. Theory Appl., 3 (2016), no. 4.
7. V. Golomoziy, Stability estimate for time-inhomogeneous Markov chains under the classical minorization condition, Theory Probab. Math. Statist., 88 (2014).
8. V. Golomoziy, Stability of time-inhomogeneous Markov chains, Bulletin of Kyiv University (Physics and Mathematical Sciences), 4 (2009), 10-15. (Ukrainian)
9. M. Kartashov, V. Golomoziy, Maximal coupling and stability of disrete Markov chains, I, Theory Probab. Math. Statist., 86 (2013), 81-92.
10. M. Kartashov, V. Golomoziiy, Maximal coupling and stability of disrete Markov chains, II, Theory Probab. Math. Statist., 87 (2013), 58-70.
11. A. Klenke, L. Mattner, Stochastic ordering of classical discrete distributions, Advances in Applied Probability, 42 (2010), no. 2, 392-410.