Large deviations of uniformly recurrent Markov additive processes
Advances in Applied Mathematics
Management Science
Elements of information theory
Elements of information theory
Queueing simulation in heavy traffic
Mathematics of Operations Research
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Performance Evaluation and Policy Selection in Multiclass Networks
Discrete Event Dynamic Systems
Approximating Martingales for Variance Reduction in Markov Process Simulation
Mathematics of Operations Research
Reliability by design in distributed power transmission networks
Automatica (Journal of IFAC)
The method of types [information theory]
IEEE Transactions on Information Theory
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We develop explicit, general bounds for the probability that the empirical sample averages of a function of a Markov chain on a general alphabet will exceed the steady-state mean of that function by a given amount. Our bounds combine simple information-theoretic ideas together with techniques from optimization and some fairly elementary tools from analysis. In one direction, motivated by central problems in simulation, we develop bounds for the general class of "geometrically ergodic" Markov chains. These bounds take a form that is particularly suited to simulation problems, and they naturally lead to a new class of sampling criteria. These are illustrated by several examples. In another direction, we obtain a new bound for the important special class of Doeblin chains; this bound is optimal, in the sense that in the special case of independent and identically distributed random variables it essentially reduces to the classical Hoeffding bound.