CAREER: Catastrophic Rare Events: Theory of Heavy Tails and Applications

The objective of this proposal is to establish a comprehensive set of tools for analyzing heavy-tailed rare events for a broad class of stochastic systems and rare events. Catastrophic rare events such as a global pandemic, market crash, and large-scale black-out have major impacts on society. Moreover, the need for understanding and controlling rare events arises frequently in many problems in statistics, science, and engineering. Remarkably, many of these seemingly disparate rare events exhibit some common characteristics: heavy-tails, large scale system dynamics, and abrupt failure of the system (catastrophe principle). Understanding the frequency and nature of such rare events is important for prevention and mitigation. The PI proposes to establish a unified theory that rigorously characterizes the catastrophe principle and develop computational and statistical tools for heavy-tailed systems.