Omar Kebiri

TL;DR: An adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem and shows that the associated semi-linear dynamic programming equations admit an equivalent formulation as a system of uncoupled forward-backward Stochastic differential equations that can be solved efficiently by a least squares Monte Carlo algorithm.

TL;DR: An adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by diffusion is proposed, based on a Gibbs variational principle that is used to determine the optimal change of measure.

TL;DR: In this article, an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion is proposed, based on a Gibbs variational principle that is used to determine the optimal (i.e., zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem.

TL;DR: In this paper, an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem is proposed. But the algorithm is not suitable for high dimensional systems.

TL;DR: It is shown that, in the same way in which the underlying dynamics can be well approximated by a reduced order effective dynamics in the time scale limit, the associated optimal expected cost converges in theTime scale limit to an effective optimal cost.