Related papers: Limit theorems under nonlinear expectations domina…
We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient.…
Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
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…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
We study the smoothness of the topological equivalence between a linear equation and its nonlinear perturbation, which is regarded as unbounded. To the best of our knowledge, it has not previously been considered such study in the…
In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.
These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity…
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on…
This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…
In this note we prove an abstract version of a result from 2002 due to Delgado and Pi\~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear…
We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of IoT applications. Our objective in this paper is to determine conditions under which a certain partially distributed system converges to…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we give a theorem about the convergence of a random series and establish a three series…