Related papers: Tightness, weak compactness of nonlinear expectati…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term…
The sub-linear expectation space is a nonlinear expectation space having advantages of modelling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace…
We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
Combining cross-section and time series data is a long and well established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two data sets. We focus on common…
We put forward a general framework for the study of a pathwise central limit theorem (CLT) and a moderate deviation principle (MDP) for stochastic partial differential equations perturbed with a small multiplicative linear noise by means of…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
The purpose of this paper is to provide tools for analyzing the compactness of sequences in Sobolev spaces, in particular if the sequence gets mapped onto a compact set by some nonlinear operator. Here, our focus lies on a very general…
This paper re-examines the limit theorems of Abadie and Imbens for nearest-neighbor matching estimators of average treatment effects with a fixed number of matches. We establish, for the first time, a non-normalized central limit theorem…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…
We discuss some basic properties of polar convergence in metric spaces. Polar convergence is closely connected with the notion of Delta-convergence of T.C. Lim known for several years. Possible existence of a topology which induces polar…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which…
In this work, we develop a numerical method to study the error estimates of the $\alpha$-stable central limit theorem under sublinear expectation with $\alpha \in(0,2)$, whose limit distribution can be characterized by a fully nonlinear…