Mathematics 697SC - ST-Comp Methods Stochastic Sys

This course presents some of the fundamental as well as state-of-the-art methods for the simulation of stochastic processes, with particular emphasis in high dimensional systems. Such stochastic models are ubiquitous in the applied sciences and engineering, arising in applications ranging from materials to biology to geophysics, economics and finance to name a few. The course will include a project component that will be selected and carried out in coordination between the instructor and the project participants. Material: 1. Introduction to Monte Carlo methods, 2. Markov Chain and Kinetic Monte Carlo methods, 3. Numerical methods for Stochastic Differential Equations, 4. Polynomial Chaos and model Reduction methods for Stochastic Partial Differential Equations, 5. Multi-level and parallelization techniques for high-dimensional stochastic systems, 6. Hybrid, multi-physics systems. Prerequisites: Knowledge of basic concepts in probability theory (Math/Stat 515), Differential Equations (Math 532 or 534) and some experience with programming.