Introduction to Rare Event Simulation

This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling. Until now, this area has had a reputation among simulation practitioners as requiring a great deal of technical and probabilistic expertise. This text keeps the mathematical preliminaries to a minimum with the only prerequisite being a single large deviation theory result that is given and proved in the text. The book contains over 50 figures and detailed simulation case studies covering a wide variety of application areas including statistics, telecommunications, and queueing systems.

Contenu

1. Random Number Generation.- 2. Stochastic Models.- 3. Large Deviation Theory.- 4. Importance Sampling.- 5. The Large Deviation Theory of Importance Sampling Estimators.- 6. Variance Rate Theory of Conditional Importance Sampling Estimators.- 7. The Large Deviations of Bias Point Selection.- 8. Chernoff's Bound and Asymptotic Expansions.- 9. Gaussian Systems.- 10. Universal Simulation Distributions.- 11. Rare Event Simulation for Level Crossing and Queueing Models.- 12. Blind Simulation.- 13. The (Over-Under) Biasing Problem in Importance Sampling.- 14. Tools and Techniques for Importance Sampling.- A. Convex Functions and Analysis.- B. A Covering Lemma.- C. Pseudo-Random Number Generator Programs.- References.