Related papers: Multivariate Stein Factors for a Class of Strongly…
The $L^k$-Wasserstein distance $\mathbb{W}_k (k\ge 1)$ and the probability distance $\mathbb{W}_\psi$ induced by a concave function $\psi$, are estimated between different diffusion processes with singular coefficients. As applications, the…
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with a measure-valued external force. We establish existence of nonnegative weak solutions satisfying gradient estimates, provided…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem…
The variance-gamma (VG) distributions form a four parameter family that includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and approximation on…
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…
This paper investigates calculations of robust funding valuation adjustment (FVA) for over the counter (OTC) derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way funding risk can be…
We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize…
We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We derive explicit bounds for the computation of normalizing constants $Z$ for log-concave densities $\pi = \exp(-U)/Z$ with respect to the Lebesgue measure on $\mathbb{R}^d$. Our approach relies on a Gaussian annealing combined with recent…
We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: arbitrary positive Dirichlet boundary conditions for the…
Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities…
In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume polynomials, is introduced: an entire function $f$ in $m$…
We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…