Related papers: Uniform approximation in classical weak convergenc…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
This paper investigates weak convergence of U-statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U-statistic exists is relaxed to having 4/3 moments only (modulo a…
Statistical convergence was introduced in connection with problems of series summation. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with…
Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to…
Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy…
We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…
The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
Asymptotic $L_p$-convergence, which resembles convergence in $L_p$, was introduced to address a question in diffusive relaxation. This note aims to compare asymptotic $L_p$-convergence with convergence in measure and in weak $L_p$ spaces.…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the…
In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure…
In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both…
We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a…
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.