Related papers: Wasserstein contraction and Poincar\'e inequalitie…

In this paper we consider a random walk of a particle in $\mathbb{R}^d$. Convergence of different transformations of trajectories of random flights with Poisson switching moments has been obtained by Davydov and Konakov, as well as…

We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of…

In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…

We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides…

Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…

We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension $d\ge 2$. The process is associated with the Dirichlet form defined by integration of the…

The behavior of slow-fast diffusions as the separation of scale diverges is a well-studied problem in the literature. In this short paper, we revisit this problem and obtain a new proof of existing strong quantitative convergence estimates…

When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…

To study diffusion processes on the p-Wasserstein space $\mathscr P_p$ for $p\in [1,\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\mathscr P_p,\Lambda)$ for…

We prove that for symmetric Markov processes of diffusion type admitting a "carr\'e du champ", the Poincar\'e inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) $\L^p(\mu)$ spaces for…

The object of study in this paper is the expected $2$-Wasserstein distance between the empirical measures of several point processes and their respective limit. For this, the main tool developed is a smoothing procedure in Euclidean spaces…

We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…

The aim of this paper is two-fold: First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (i) for all $n\ge1$, the diffusion matrix $A$ is weak upper semicontinuous on $\Omega$ if and only if…

This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of…

We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…

We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global…

In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's…

For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…

Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction…