Rare-event Analysis and Computational Methods for Stochastic Systems Driven by Random Fields (RESEARCH AREA 3)
Abstract
This proposal will investigate asymptotic theories and the corresponding numerical methods for computing rare-event probabilities associated with random fields and the associated random elliptical PDEs. This proposal will perform risk analysis of stochastic systems by investigating the asymptotic behavior of certain interesting rare events. For instance, assessment will be conducted and efficient numerical methods will be developed for the risk of material s not being able to support a certain amount of external force and of predicting the major causes of material failure. A central methodological idea will be to develop limit theorems of complex functionals of spatial processes and further take advantage of the asymptotic results in order to guide construction of efficient Monte Carlo methods that can be applied in the pre-limit. The work will exploit the development of random field asymptotics, will develop asymptotic results guided by physical intuition and existing strategies, extract the main features underlying this asymptotic analysis, interpret them in terms of Monte Carlo methods, and then establish the rigorous efficiency of those methods.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510159
Entities
People
- Jingchen Liu
Organizations
- Army Contracting Command
- Columbia University
- United States Army