Related papers: Importance sampling for stochastic reaction-diffus…

We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale…

In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the…

In this article, we address the issues that come up in the design of importance sampling schemes for rare events associated to stochastic dynamical systems. We focus on the issue of metastability and on the effect of multiple scales. We…

We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time,…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…

Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…

The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…

Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…

Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling in the framework of diffusion process and consider the change…

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of…