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.
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