Related papers: Limits for Partial Maxima of Gaussian Random Vecto…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity.…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…
Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
Motivated by the papers of Mladenovc and Piterbarg (2006), Krajka (2011) and Pereira and Tan (2017), we study the limit properties for the maxima from nonstationary random fields subject to missing observations and obtain the weakly…
A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-dynamical system corresponding to these expansions. Then,…
In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and…
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as…
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order…
In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable…
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on…
In \cite{BNT}, a framework to prove almost sure central limit theorems for sequences $(G_n)$ belonging to the Wiener space was developed, with a particular emphasis of the case where $G_n$ takes the form of a multiple Wiener-It\^o integral…
We study the scaling limit and prove the law of large numbers for weakly pinned Gaussian random fields under the critical situation that two possible candidates of the limits exist at the level of large deviation principle. This paper…