相关论文: Faster Evaluation of Multidimensional Integrals

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…

Efficiently pricing multi-asset options poses a significant challenge in quantitative finance. Fourier methods leverage the regularity properties of the integrand in the Fourier domain to accurately and rapidly value options that typically…

This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one…

A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of…

For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…

A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…

In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…

The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J…

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the…

Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…

It has been found empirically that quasi-Monte Carlo methods are often efficient for very high-dimensional problems, that is, with dimension in the hundreds or even thousands. The common explanation for this surprising fact is that those…

Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…

This paper concerns the use of a particular class of determinantal point processes (DPP), a class of repulsive spatial point processes, for Monte Carlo integration. Let $d\ge 1$, $I\subseteq \overline d=\{1,\dots,d\}$ with $\iota=|I|$.…

Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…

We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…

We use the technique of information relaxation to develop a duality-driven iterative approach to obtaining and improving confidence interval estimates for the true value of finite-horizon stochastic dynamic programming problems. We show…