Related papers: Escaping from an attractor: Importance sampling an…
In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal…
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an $\alpha $-stable process. It is proved that extremal solutions are selected and the respective…
We demonstrate the possibility to systematically steer the most probable escape paths (MPEPs) by adjusting relative noise intensities in dynamical systems that exhibit noise-induced escape from a metastable point via a saddle point. Using a…
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…
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…
Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its…
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…
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…
A new approach for the weak noise analysis of exit problems removes an intrinsic contradiction of an existing method. It applies for both the mean time and the location of the exits; novel outcomes mainly concern the exits from entire…
Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between…
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
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…
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…