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One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…

Statistics Theory · Mathematics 2024-12-20 Fabian Mies

A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results for linear and quadratic functionals of…

Probability · Mathematics 2016-08-16 Giovanni Peccati , Igor Prünster

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the…

Probability · Mathematics 2015-12-07 Richard C. Bradley , Cristina Tone

We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk…

Analysis of PDEs · Mathematics 2024-11-20 Roberta Marziani , Francesco Solombrino

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

Statistics Theory · Mathematics 2025-04-09 Moritz Jirak , Alois Kneip , Alexander Meister , Mario Pahl

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…

Statistics Theory · Mathematics 2015-07-28 Randolf Altmeyer , Markus Bibinger

\noindent The paper establishes weak convergence in $C[0,1]$ of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both…

Probability · Mathematics 2015-04-30 Shuyang Bai , Mamikon S. Ginovyan , Murad S. Taqqu

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein's method,…

Probability · Mathematics 2013-03-12 Viet Hung Pham

This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting…

Probability · Mathematics 2021-04-30 Vitalii Makogin , Evgeny Spodarev

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural…

Probability · Mathematics 2018-07-25 Erwan Koch , Clément Dombry , Christian Y. Robert

We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa\la and Weso\lowski (Statist. Probab.…

Probability · Mathematics 2015-05-21 Kamil Marcin Kosiński

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…

Probability · Mathematics 2014-12-25 Tomasz Schreiber , Christoph Thaele

We consider sequences of needlet random fields defined as weighted averaged forms of spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for the boundary lengths of their excursion sets.…

Probability · Mathematics 2020-11-06 Radomyra Shevchenko , Anna Paola Todino

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…

Statistics Theory · Mathematics 2016-01-07 S. N. Lahiri , Peter M. Robinson

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to…

Probability · Mathematics 2007-05-24 Nadine Guillotin-Plantard , Arnaud Le Ny

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…

Statistics Theory · Mathematics 2023-12-25 Roberto Pereira , Xavier Mestre , David Gregoratti

We prove a central limit theorem for smooth linear statistics related to the zero divisors of Gaussian i.i.d. centered holomorphic sections of tensor powers of a Hermitian holomorphic line bundle over a non-compact Hermitian manifold.

Complex Variables · Mathematics 2026-05-05 Afrim Bojnik , Ozan Günyüz

This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…

Probability · Mathematics 2022-02-08 Illia Donhauzer , Andriy Olenko

The results on $\Gamma$-limits of sequences of free-discontinuity functionals with bounded cohesive surface terms are extended to the case of vector-valued functions. In this framework, we prove an integral representation result for the…

Analysis of PDEs · Mathematics 2026-01-27 Gianni Dal Maso , Davide Donati