Related papers: Stratified Monte Carlo quadrature for continuous r…
The paper describes the practical work for students visually clarifying the mechanism of the Monte Carlo method applying to approximating the value of Pi. Considering a traditional quadrant (circular sector) inscribed in a square, here we…
Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…
We consider the problem of estimating the density of a random variable $X$ that can be sampled exactly by Monte Carlo (MC). We investigate the effectiveness of replacing MC by randomized quasi Monte Carlo (RQMC) or by stratified sampling…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
We implement a discretization of the one-dimensional branching Brownian motion in the form of a Monte Carlo event generator, designed to efficiently produce ensembles of realizations in which the rightmost lead particle at the final time…
For numerical approximations to stochastic differential equations using the Euler-Maruyama scheme, we propose incorporating approximate random variables computed using low precisions, such as single and half precision. We propose and…
For qubits, Monte Carlo estimation of the average fidelity of Clifford unitaries is efficient -- it requires a number of experiments that is independent of the number $n$ of qubits and classical computational resources that scale only…
Monte Carlo sampling techniques are used to estimate high-dimensional integrals that model the physics of light transport in virtual scenes for computer graphics applications. These methods rely on the law of large numbers to estimate…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of…
We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically optimal in the sense that it requires $\tilde{O}(d)$ (up to…
Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications…
Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…