Rare Event Simulation using Monte Carlo Methods
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.\...
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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.
Contributors viiPreface ix1 Introduction to Rare Event Simulation Gerardo Rubino Bruno Tuffin 1Part I Theory 152 Importance Sampling in Rare Event Simulation Pierre L'Ecuyer Michel Mandjes Bruno Tuffin 173 Splitting Techniques Pierre L'Ecuyer François Le Gland Pascal Lezaud Bruno Tuffin 394 Robustness Properties and Confidence Interval Reliability Issues Peter W. Glynn Gerardo Rubino Bruno Tuffin 63Part II Applications 855 Rare Event Simulation for Queues José Blanchet Michel Mandjes 876 Markovian Models for Dependability Analysis Gerardo Rubino Bruno Tuffin 1257 Rare Event Analysis by Monte Carlo Techniques in Static Models Héctor Cancela Mohamed El Khadiri Gerardo Rubino 1458 Rare Event Simulation and Counting Problems José Blanchet Daniel Rudoy 1719 Rare Event Estimation for a Large-Scale Stochastic Hybrid System with Air Traffic Application Henk A. P. Blom G. J. (Bert) Bakker Jaroslav Krystul 19310 Particle Transport Applications Thomas Booth 21511 Rare Event Simulation Methodologies in Systems Biology Werner Sandmann 243Index 267
