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In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

We derive and analyze numerical methods for underdamped (kinetic) Langevin dynamics in a domain with elastic reflection at the boundary. First-order approximations are based on an Euler-type scheme incorporating collision-handling at the…

We examine the use of different randomisation policies for stochastic gradient algorithms used in sampling, based on first-order (or overdamped) Langevin dynamics, the most popular of which is known as Stochastic Gradient Langevin Dynamics.…

Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…

A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

The random splitting Langevin Monte Carlo could mitigate the first order bias in Langevin Monte Carlo with little extra work compared other high order schemes. We develop in this work an analysis framework for the sampling error under…

In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…

We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…

As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from slow convergence…

In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch…

We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…

Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…

We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…

The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…

We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…