Rare Event Simulation Methodologies and Applications

Stochastic models are widely used in a large diversity of application areas. In many important cases the underlying system’s behavior is strongly influenced by rare events, which occur with extremely small probability but which may have serious consequences. The necessity to analyze such rare events is exemplified by ruins in insurance risk or finance, breakdowns of manufacturing systems, packet losses and buffer overflows in computer and communication networks, false alarms in radar or similar security systems, technical defects, amongst many others. Analytical and numerical treatment of realistically dimensioned system models involving rare events is usually infeasible and the modeling power and flexibility of stochastic simulation provides several advantages over other approaches. However, brute force direct simulation of rare events is not effective, since rare events occur too infrequently in simulations to compute reliable statistical estimates in reasonable time. Hence, specialized rare event simulation techniques are highly desirable. Simulation speed-up is necessary in the sense that the simulation time to obtain estimates with appropriate accuracy must be reduced. In recent years, there have been significant theoretical and practical advances towards the development of efficient simulation techniques for the evaluation of systems involving rare events. The remarkable success and the effectiveness of methodologies for rare event simulation have led to more research into their potential as well as a growing interest in their accessibility and robustness. The continuously increasing complexity of real world systems poses demanding challenges for the development of advanced rare event simulation methodologies and their applications. Importance sampling and RESTART (Repetitive Simulation Trials after Reaching Thresholds), which is a variant of importance splitting, are the most widespread rare event simulation techniques. In order to achieve variance reduction, importance sampling applies a change of measure such that the rare event of interest occurs more frequently