Konstantinos Spiliopoulos - BU

Starts: 4:00 pm on Thursday, September 20, 2012
Ends: 5:00 pm on Thursday, September 20, 2012
Location: MCS 148

Title: Escaping from an attractor: importance sampling and rest points. Abstract: Questions like understudying transitions between metastable equilibrium states of stochastic dynamical systems and computing transition times have attracted a lot of attention in both the the probability and applied mathematics community and at the same time are generic questions in disciplines such as chemical physics and biology. However, despite the substantial developments of the last five decades in both theory and algorithms, very little is known on how to design and rigorously analyze provably efficient Monte Carlo methods for rare event problems, like probability of escape from an equilibrium and transition to another one, when rest points play a key role. Even though several algorithms do exist, they have been applied only to specific systems and have not been rigorously analyzed. Therefore, it is not well understood when they work well and how to efficiently design them. In this talk, I will discuss importance sampling Monte Carlo schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. We build importance sampling schemes with provably good performance both pre-asymptotically, i.e., for fixed size of the noise, and asymptotically, i.e., as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Extensive simulation studies demonstrated the theoretical results.