Related papers: Importance Sampling for Multiscale Diffusions
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 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 develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
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…
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 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…
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…
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting…
This paper considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for e.g. modelling of credit risk. Previous attempts at designing importance sampling algorithms…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…