Abstract
We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a highly reliable Markovian system. Also, a class of importance sampling methods is defined for which we prove a necessary and sufficient condition for bounded relative error for the performance measure estimator. This class of probability measures includes all of the currently existing failure biasing methods in the literature. Similar conditions for derivative estimators are established.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 687-727 |
| Number of pages | 41 |
| Journal | Advances in Applied Probability |
| Volume | 28 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1996 |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Statistics and Probability
Keywords
- Gradient estimation
- Importance sampling
- Likelihood ratios
- Markov chains
- Reliability
- Simulation