Rare Events in Stochastic Systems
Subtitle: Modeling, Simulation Design and Algorithm Analysis
By: Yixi Shi
Publisher: [publisher not identified]
Published: 2013
Place of publication: [New York, N.Y.?]
Language: eng
Description: This dissertation explores a few topics in the study of rare events in stochastic systems, with a particular emphasis on the simulation aspect. This line of research has been receiving a substantial amount of interest in recent years, mainly motivated by scientific and industrial applications in which system performance is frequently measured in terms of events with very small probabilities.The topics mainly break down into the following themes: Algorithm Analysis: Chapters 2, 3, 4 and 5. Simulation Design: Chapters 3, 4 and 5. Modeling: Chapter 5. The titles of the main chapters are detailed as follows: Chapter 2: Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks Chapter 3: Splitting for Heavy-tailed Systems: An Exploration with Two Algorithms Chapter 4: State Dependent Importance Sampling with Cross Entropy for Heavy-tailed Systems Chapter 5: Stochastic Insurance-Reinsurance Networks: Modeling, Analysis and Efficient Monte Carlo.
Notes: Department: Industrial Engineering and Operations Research.

Thesis advisor: Jose Blanchet.

Thesis (Ph.D.)--Columbia University, 2013.