The blind simulation problem and regenerative processes

Blind simulation techniques are Monte Carlo simulation strategies that can be carried out with little or no knowledge of the underlying probability law. We first show (in the independent and identically distributed setting) that by a strategy of selectively throwing away data samples, we can achieve arbitrarily close to the optimal performance gains promised by the importance sampling strategy known as quick simulation. In our attempt to generalize our results to Markovian structures, we are led necessarily to a consideration of their regeneration structure and hence to a general consideration of regenerative processes. We derive several new large deviation results for these processes. Using these techniques we then demonstrate the same surprising results hold for many regenerative processes.