Related papers: Extremes of vector-valued Gaussian processes: exac…

We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…

We consider canonical determinantal random point processes with N particles on a compact Riemann surface X defined with respect to the constant curvature metric. In the higher genus (hyperbolic) cases these point processes may be defined in…

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…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

We derive, up to a constant factor, matching lower and upper bounds on the concentration functions of suprema of separable centered Gaussian processes and order statistics of Gaussian random fields. These bounds reveal that suprema of…

For suitable families of locally infinitely divisible Markov processes $\{\xi^{{\epsilon}}_t\}_{0\leq t\leq T}$ with frequent small jumps depending on a small parameter $\epsilon>0,$ precise asymptotics for large deviations of integral…

With $\{\xi_i\}_{i\ge 0}$ being a centered stationary Gaussian sequence with non-negative correlation function $\rho(i):=\mathbb{E}[ \xi_0\xi_i]$ and $\{\sigma(i)\}_{i\ge 1}$ a sequence of positive reals, we study the asymptotics of the…

We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.

This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…

We give a dimension-independent sparsification result for suprema of centered Gaussian processes: Let $T$ be any (possibly infinite) bounded set of vectors in $\mathbb{R}^n$, and let $\{\boldsymbol{X}_t := t \cdot \boldsymbol{g} \}_{t\in…

We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…

Let X be a generalised symmetrised Dirichlet random vector in R^k, and let u_n be thresholds such that P{X> u_n} tends to 0 as n goes infinity. In this paper we derive an exact asymptotic expansion of P{X> u_n} assuming that the associated…

We give a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms, etc. Most attention is…

Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

Non-stationary approximations of the final value of a converging sequence are discussed, and we show that extremal eigenvalues can be reasonably estimated from the CG iterates without much computation at all. We introduce estimators of…

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…