Rare Event Simulation using Monte Carlo Methods

Wiley | 2009 | ISBN: 0470772697 | 280 pages | PDF | 1,5 MB

In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue.


Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics.

Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.

Contents

Contributors vii

Preface ix

1 Introduction to Rare Event Simulation 1

Gerardo Rubino and Bruno Tuffin

PART I THEORY 15

2 Importance Sampling in Rare Event Simulation 17

Pierre L’Ecuyer, Michel Mandjes and Bruno Tuffin

3 Splitting Techniques 39

Pierre L’Ecuyer, Fran¸cois Le Gland, Pascal Lezaud

and Bruno Tuffin

4 Robustness Properties and Confidence Interval Reliability

Issues 63

Peter W. Glynn, Gerardo Rubino and Bruno Tuffin

PART II APPLICATIONS 85

5 Rare Event Simulation for Queues 87

Jos´e Blanchet and Michel Mandjes

6 Markovian Models for Dependability Analysis 125

Gerardo Rubino and Bruno Tuffin

7 Rare Event Analysis by Monte Carlo Techniques in Static Models 145

H´ector Cancela, Mohamed El Khadiri and Gerardo Rubino

8 Rare Event Simulation and Counting Problems 171

Jos´e Blanchet and Daniel Rudoy

9 Rare Event Estimation for a Large-Scale Stochastic Hybrid

System with Air Traffic Application 193

Henk A. P. Blom, G. J. (Bert) Bakker and Jaroslav Krystul

10 Particle Transport Applications 215

Thomas Booth

11 Rare Event Simulation Methodologies in Systems Biology 243

Werner Sandmann

Index 267

   
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