Related papers: \epsilon-Strong simulation of the Brownian path

We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…

We introduce modifications to Monte Carlo simulations of the Feynman path integral that improve sampling of localised interactions. The new algorithms generate trajectories in simple background potentials designed to concentrate them about…

We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Bayesian optimization (BO) is a powerful framework for estimating parameters of expensive simulation models, particularly in settings where the likelihood is intractable and evaluations are costly. In stochastic models every simulation is…

We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach…

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…

We present a novel control variate technique for enhancing the efficiency of Monte Carlo (MC) estimation of expectations involving solutions to stochastic differential equations (SDEs). Our method integrates a primary fine-time-step…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…

We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random…

Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…