Related papers: Wasserstein convergence rates in the invariance pr…

The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

We show the convergence of the zero relaxation limit in systems of $2 \times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation…

Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…

It is known that if a sequence of domains $U_n$ converges to a domain $U$ in the Caratheodory sense then the hyperbolic densities on $U_n$ converge to the hyperbolic density on $U$. In this paper, we study the rate of convergence of the…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

We study the local convergence of diffusive mean-field systems, including Wasserstein gradient flows, min-max dynamics, and multi-species games. We establish exponential local convergence in $\chi^2$-divergence with sharp rates, under two…

We consider a class of piecewise hyperbolic maps from the unit square to itself preserving a contracting foliation and inducing a piecewise expanding quotient map, with infinite derivative (like the first return maps of Lorenz like flows).…

For $\ell\colon \mathbb{R}^d \to [0,\infty)$ we consider the sequence of probability measures $\left(\mu_n\right)_{n \in \mathbb{N}}$, where $\mu_n$ is determined by a density that is proportional to $\exp(-n\ell)$. We allow for infinitely…

We study inhomogeneous non-strictly hyperbolic systems of two equations, which are a formal generalization of the transformed one-dimensional Euler-Poisson equations. For such systems, a complete classification of the behavior of the…

A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…

This paper establishes a complete homogenization theory for the one-dimensional parabolic equation with long-range correlated random potential: \[ \partial_t u_\varepsilon(t,x) = \frac{1}{2} \partial_{xx} u_\varepsilon(t,x) +…

This paper extends the model reduction method by the operator projection to the one-dimensional special relativistic Boltzmann equation. The derivation of arbitrary order globally hyperbolic moment system is built on our careful study of…

Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…

The central limit theorem is one of the most fundamental results in probability and has been successfully extended to locally dependent data and strongly-mixing random fields. In this paper, we establish its rate of convergence for…

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

We consider the hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…

We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…