Related papers: On some Non Asymptotic Bounds for the Euler Scheme

It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

In this article, we give sharp bounds for the Euler- and trapezoidal discretization of the Levy area associated to a d-dimensional fractional Brownian motion. We show that there are three different regimes for the exact root mean-square…

Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit…

We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…

In this paper, we prove convergence rates for time discretisation schemes for semi-linear stochastic evolution equations with additive or multiplicative Gaussian noise, where the leading operator $A$ is the generator of a strongly…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural…

We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…

In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion…

Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…

We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on the space of square-integrable functions, whose…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…

We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white noise. The new method can easily be combined with a finite…

We prove an extension of McDiarmid's inequality for metric spaces with unbounded diameter. To this end, we introduce the notion of the {\em subgaussian diameter}, which is a distribution-dependent refinement of the metric diameter. Our…

We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…

In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…

In this article we consider a Monte Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…