相关论文: On efficient weighted integration via a change of …

Pre-integration is an extension of conditional Monte Carlo to quasi-Monte Carlo and randomized quasi-Monte Carlo. It can reduce but not increase the variance in Monte Carlo. For quasi-Monte Carlo it can bring about improved regularity of…

In this paper we study parabolic stochastic partial differential equations defined on arbitrary bounded domain $\cO \subset \bR^d$ allowing Hardy inequality: $$ \int_{\cO}|\rho^{-1}g|^2\,dx\leq C\int_{\cO}|g_x|^2 dx, \quad \forall g\in…

Quasi-Monte Carlo cubature methods often sample the integrand using Sobol' (or other digital) sequences to obtain higher accuracy than IID sampling. An important question is how to conservatively estimate the error of a digital sequence…

We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…

Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1/8 doped two-dimensional Hubbard model with imposed uni-directional stripe-like charge density wave modulation. We find a significant…

We consider the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leq…

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…

In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…

We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic dependence on the parameters as considered in [Cl.~Schillings…

Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…

Conditional Monte Carlo (CMC) has been widely used for sensitivity estimation with discontinuous integrands as a standard simulation technique. A major limitation of using CMC in this context is that finding conditioning variables to ensure…

Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field…

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for…

We study the boundary charge $Q_B$ of generic semi-infinite one-dimensional insulators with translational invariance and show that non-local symmetries (i.e., including translations) lead to rational quantizations $p/q$ of $Q_B$. In…

A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at…

In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the…