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In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order…

Statistics Theory · Mathematics 2020-06-18 L. Douge

We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of…

Complex Variables · Mathematics 2007-05-23 Mikhail Sodin , Boris Tsirelson

This paper analyzes over 30 types of q-series and the asymptotic behavior of their expansions. A method is described for deriving further asymptotic formulas using convolutions of generating functions with subexponential growth. All…

Combinatorics · Mathematics 2016-03-08 Vaclav Kotesovec

Our main aim is to apply the theory of regularly varying functions to the asymptotical analysis at infinity of solutions of Friedmann cosmological equations. A new constant $\Gamma$ is introduced related to the Friedmann cosmological…

General Relativity and Quantum Cosmology · Physics 2017-03-21 Žarko Mijajlović , Nadežda Pejović , Stevo Šegan , Goran Damljanović

This paper establishes new results concerning asymptotic expansions of $q$-series related to partial theta functions. We first establish a new method to obtain asymptotic expansions using a result of Ono and Lovejoy, and then build on these…

Number Theory · Mathematics 2025-12-09 Alexander E. Patkowski

We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation of different modes in the Landau limit, and implements a correct…

High Energy Physics - Theory · Physics 2021-07-22 Benjamin Knorr

Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…

Statistics Theory · Mathematics 2022-01-03 Fan Zhou , Ping Li , Cun-Hui Zhang

We investigate the asymptotic expansion of integrals analogous to Ball's integral \[\int_0^\infty \left(\frac{\Gamma(1+\nu)|J_\nu(x)|}{(x/2)^\nu}\right)^{\!n}dx\] for large $n$ in which the Bessel function $J_\nu(x)$ is replaced by the…

Classical Analysis and ODEs · Mathematics 2021-02-05 R B Paris

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…

General Mathematics · Mathematics 2007-05-23 Brice Camus

We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under consideration has fractional order $2s \in (0,1)$ and a first-order…

Analysis of PDEs · Mathematics 2024-10-31 Serena Dipierro , Enrico Valdinoci , Mary Vaughan

We obtain the asymptotic expansion of the Voigt functions $K(x,y)$ and $L(x,y)$ for large (real) values of the variables $x$ and $y$, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered…

Classical Analysis and ODEs · Mathematics 2014-04-01 R B Paris

This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…

Methodology · Statistics 2012-02-02 Timothy B. Armstrong

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…

Statistics Theory · Mathematics 2020-12-01 Laura Dumitrescu , Ioana Schiopu-Kratina

A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…

Analysis of PDEs · Mathematics 2022-08-12 Taras A. Mel'nyk , Arsen V. Klevtsovskiy

We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor $Y$. Assuming the data in question is invariant under an…

Differential Geometry · Mathematics 2016-08-24 Julius Ross , Michael Singer

The paper concerned with higher order asymptotic expansion of solutions to the Cauchy problem of abstract hyperbolic equations of the form $u''+Au+u'=0$ in a Hilbert space, where $A$ is a nonnegative selfadjoint operator. The result says…

Analysis of PDEs · Mathematics 2021-05-21 Motohiro Sobajima

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…

Statistics Theory · Mathematics 2011-04-04 L. Gardes , S. Girard , A. Lekina

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Probability · Mathematics 2013-12-10 Sergio Albeverio , Boubaker Smii

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…

Probability · Mathematics 2017-10-10 E. Ostrovsky , L. Sirota

An asymptotic formula is proved for the k-fold divisor function averaged over homogeneous polynomials of degree k in k-1 variables coming from incomplete norm forms.

Number Theory · Mathematics 2016-09-22 Valentin Blomer