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Center for Nonlinear Studies |
Many rare events in man-made networks exhibit heavy-tailed features. Examples are file sizes, delays and financial losses, but also magnitudes of systemic events, such as the size of a blackout in a power grid. The theory of rare events in the heavy-tailed case is not as well developed as it is for light-tailed systems: apart from a few isolated examples, it is restricted to events that are caused by a single big jump. In this work, we develop sample-path large deviations for random walks and Levy processes in the heavy-tailed case that go beyond such restrictions. We show that for such systems, the rare event is not characterized by the solution of a variational problem as it would be in the light-tailed case, but by an impulse control problem. These insights are used to develop a generic importance sampling technique that has bounded relative error, is applicable to any continuous functional of a (collection of) random walks, and is tested on several models. Joint work with Jose Blanchet (Stanford), Chang-Han Rhee, and Bohan Chen.
Host: Michael Chertkov