An Introduction to Rare Event Simulation (Springer Series in Statistics) （2004. XI, 260 p. w. 50 figs. 24,5 cm）

Bucklew, James

SPRINGER, BERLIN（2004発売）

• 製本 Hardcover:ハードカバー版／ページ数 270 p.
• 商品コード 9780387200781

Full Description

This book is an attempt to present a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. This framework allows us to view a vast assortment of simulation problems from a single unified perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Unfortunately, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. In this text, I have tried to keep the mathematical preliminaries to a minimum; the only prerequisite is a single large deviation theorem dealing with sequences of Rd­ valued random variables. (This theorem and a proof are given in the text.) Large deviation theory is a burgeoning area of probability theory and many of the results in it can be applied to simulation problems. Rather than try to be as complete as possible in the exposition of all possible aspects of the available theory, I have tried to concentrate on demonstrating the methodology and the principal ideas in a fairly simple setting. Madison, Wisconsin 2003 James Antonio Bucklew Contents 1. Random Number Generation . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1.1 Uniform Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Nonuniform Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 The Inversion Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 The Acceptance---Rejection Method . . . . . . . . . . . . 10 . . . . . 1.3 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . 13 . . . . . . . . . . . 1.3.1 Inversion by Truncation of a ContinuousAnalog. . . . . . 14 1.3.2 Acceptance---Rejection . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . .

Contents

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.