Related papers: On the randomized Euler algorithm under inexact in…

In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings.…

The present work introduces and investigates an explicit time discretization scheme, called the projected Euler method,to numerically approximate random periodic solutions of semi-linear SDEs under non-globally Lipschitz conditions. The…

We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.

In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by L\'evy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of…

This paper is concerned with the numerical integration of stochastic differential equations (SDEs) which govern diffusion processes driven by a standard Wiener process. With the latter being replaced by a sequence of increments at discrete…

Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…

We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…

This paper revisits the well known single machine scheduling problem to minimize total weighted completion times. The twist is that job sizes are stochastic from unknown distributions, and the scheduler has access to only a single sample…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…

In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift. In particular, the drift is assumed to be $\alpha$-H\"older continuous in time and bounded…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

The issue of single-grid discretization error estimator, operating in the postprocessor mode, is addressed in the paper. An ensemble of numerical solutions, obtained using solvers of different accuracy, is shown to provide an upper estimate…

Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not…

In coherent optical communication systems the laser phase noise is commonly modeled as a Wiener process. We propose a sliding-window based linearization of the phase noise, enabling a novel description. We show that, by stochastically…

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…

We employ the variational formulation and the Euler-Lagrange equations to study the steady-state error in linear non-causal estimators (smoothers). We give a complete description of the steady-state error for inputs that are polynomial in…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…