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Upper and lower bounds for the solutions of Markov renewal equations. (English) Zbl 1101.60066
Summary: Upper and lower bounds are studied for the solutions of Markov renewal equations. Some of their special cases are derived under specific marginal conditions and in an alternating environment. The method to construct the bounds is also explained in detail. At the end, these bounds are applied to a shock model and an age-dependent branching process under Markovian environment.

MSC:
60K05 Renewal theory
90C40 Markov and semi-Markov decision processes
65C50 Other computational problems in probability (MSC2010)
60E15 Inequalities; stochastic orderings
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