Related papers: Minimising MCMC variance via diffusion limits, wit…

Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori…

We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…

In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…

The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…

This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…

We explain the fundamental challenges of sampling from multimodal distributions, particularly for high-dimensional problems. We present the major types of MCMC algorithms that are designed for this purpose, including parallel tempering,…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

Model Predictive Control (MPC) is well understood in the deterministic setting, yet rigorous stability and performance guarantees for stochastic MPC remain limited to the consideration of terminal constraints and penalties. In contrast,…

Many practical applications of optimal control are subject to real-time computational constraints. When applying model predictive control (MPC) in these settings, respecting timing constraints is achieved by limiting the number of…

Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform…

We develop a new simulation method for multidimensional diffusions with sticky boundaries. The challenge comes from simulating the sticky boundary behavior, for which standard methods like the Euler scheme fail. We approximate the sticky…

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…

Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…

Simulated tempering (ST) has attracted a great deal of attention in the last years, due to its capability to allow systems with complex dynamics to escape from regions separated by large entropic barriers. However its performance is…

We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC…