Mathematics 797RE - ST-Model,Simulatn&UncertQuant

We discuss first what are rare events, why are they important, how are they modeled and why their simulation is a significant high performance computing challenge. We will discuss some of the existing methods and will apply them in prototype systems in applications selected from (among others) queueing theory, molecular dynamics, biochemical reaction networks and finance. Furthermore, we will discuss mathematical theories for rare events and in particular elements of the theory of large deviations and its insights in providing better sampling algorithms for rare events. Finally, will also discuss recent progress on the uncertainty quantification and sensitivity analysis of rare events, that allow us to assess their impact on the predictions of statistical models.

Open to Graduate students only. Pre-requisites for this course are:
1) Stat 607 or Stat 605
2) Math 623 or Stat 605 or equivalent (check with instructor)
3) Math 532H or Math 645 or any class in stochastic processes