Related papers: Computing Functionals of Multidimensional Diffusio…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
In this article, we present a review of the recent developments on the topic of Multilevel Monte Carlo (MLMC) algorithm, in the paradigm of applications in financial engineering. We specifically focus on the recent studies conducted in two…
The application of the diffusion Monte Carlo method to a strongly interacting Fermi system as normal liquid $^3$He is explored. We show that the fixed-node method together with the released-node technique and a systematic method to…
We show that reaction-diffusion processes in three dimensions can be efficiently handled by event-driven numerical simulations, based on statistical waiting times (Gillespie's Monte-Carlo method). The algorithm is efficient for dilute…
We developed a Monte Carlo simulation method to calculate incoherent Thomson scattering spectra in high temperature plasmas. The basic idea is to treat the entire scattering process as the superposition of individual photon-electron…
We present a novel way of performing kinetic Monte Carlo simulations which does not require an {\it a priori} list of diffusion processes and their associated energetics and reaction rates. Rather, at any time during the simulation,…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
The paper proposes Monte Carlo algorithms for the computation of the information rate of two-dimensional source/channel models. The focus of the paper is on binary-input channels with constraints on the allowed input configurations. The…
We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and…
This paper uses Lie symmetry methods to calculate certain expectations for a large class of It\^{o} diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form $E_x(e^{-\lambda…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
In this paper, we present a very fast Monte Carlo scheme for additive processes: the computational time is of the same order of magnitude of standard algorithms for Brownian motions. We analyze in detail numerical error sources and propose…
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…
We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in…
We discuss multivariate Monte Carlo methods appropriate for X-ray dispersive spectrometers. Dispersive spectrometers have many advantages for high resolution spectroscopy in the X-ray band. Analysis of data from these instruments is…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…
We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorithm samples the underlying probability space and evolves these…
The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…