Abstract
Consider the normalized partial sums of a real-valued function F of a Markov chain,
1. It is known that this drift condition is equivalent to the existence of a unique invariant distribution π satisfying π(W)<∞, and the law of large numbers holds for any function F dominated by W:
2. The lower error probability defined by
3. If W is near-monotone, then control-variates are constructed based on the Lyapunov function V, providing a pair of estimators that together satisfy nontrivial large asymptotics for the lower and upper error probabilities.
In an application to simulation of queues it is shown that exact large deviation asymptotics are possible even when the estimator does not satisfy a central limit theorem.
Citation
Sean P. Meyn. "Large deviation asymptotics and control variates for simulating large functions." Ann. Appl. Probab. 16 (1) 310 - 339, February 2006. https://doi.org/10.1214/105051605000000737
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