相关论文: Multidimensional sampling for simulation and integ…
In this survey paper we discuss some tools and methods which are of use in quasi-Monte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with $d$-dimensions and derivatives of order…
We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo…
We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems. We obtain our…
We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the variable of integration is drawn from a mixture distribution as…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…
This paper proposes a new importance sampling (IS) that is tailored to quasi-Monte Carlo (QMC) integration over $\mathbb{R}^s$. IS introduces a multiplicative adjustment to the integrand by compensating the sampling from the proposal…
Antithetic sampling, which goes back to the classical work by Hammersley and Morton (1956), is one of the well-known variance reduction techniques for Monte Carlo integration. In this paper we investigate its application to digital nets…
In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
We study quasi-Monte Carlo (QMC) integration over the multi-dimensional unit cube in several weighted function spaces with different smoothness classes. We consider approximating the integral of a function by the median of several integral…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…