ABSTRACT

Monte-Carlo estimates for skip-free Markov chains exhibit surprisingly exotic 
behavior.  For example, simulation of the mean of a Reflected Random Walk (RRW)
exhibits non-standard behavior, even for light-tailed increment distributions 
with negative drift. The Large Deviation Principle (LDP) holds for deviations 
below the mean, but for deviations at the usual speed, above the mean the rate 
function is null. Similar results hold for "norm like" function of a skip-free 
Markov chain.

This talk takes a deeper look at these results for the RRW. A complete sample 
path LDP analysis is described that helps to explain why simulating a RRW is 
hard. This gives rise to non-convex rate function and elegant concave most likely 
paths. Similar qualitative results are obtained for more general classes of 
Markov models.  

These results suggest new ways of designing control variates to construct a pair 
of estimators that provide upper and lower confidence bounds in simulation.