Application of importance sampling to the computation of large deviations in nonequilibrium processes.

AN ADAPTIVE IMPORTANCE SAMPLING-BASED ALGORITHM USING THE FIRST-ORDER METHOD FOR STRUCTURAL RELIABILITY

Monte Carlo simulation (MCS) is a useful tool for computation of probability of failure in reliability analysis. However, the large number of samples, often required for acceptable accuracy, makes it time-consuming. Importance sampling is a method on the basis of MCS which has been proposed to reduce the computational time of MCS. In this paper, a new adaptive importance sampling-based algorith...

Quenched large deviations for multiscale diffusion processes in random environments*

We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium is assumed to be stationary and ergodic. In the course of the proof we also prove related quenched ergodic theorems for controlled diffusion processes in ra...

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(Xε(t)) : ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X(t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ...

Nonequilibrium Markov Processes Conditioned on Large Deviations

Importance sampling and theory of nonequilibrium solvation dynamics in water

We have devised a novel importance sampling method for nonequilibrium processes. Like transition path sampling, the method employs a Monte Carlo procedure to confine or bias the search through trajectory space. In this way, molecular dynamics trajectories consistent with the nonequilibrium dynamics of interest are generated efficiently. Using results of this sampling, we demonstrate that statis...