Related papers: Extremes of Chi-square Processes with Trend

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary…

For $X_i(t), i=1,\ldots, n, t\in [0,T]$ centered Gaussian processes, the chi-square process $\sum_{i=1}^{n}X_i^2(t)$ appears naturally as limiting processes in various statistical models. In this paper, we are concerned with the exact tail…

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima.…

This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…

This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times…

In this paper, we analyze a multivariate counterpart of the generalized weighted Kolmogorov-Smirnov statistic, which is the supremum of weighted locally stationary chi-square process over non-compact interval. The boundedness and the exact…

Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector,…

This contribution derives the exact asymptotic behaviour of the supremum of alpha(t)-locally stationary Gaussian random fields over a finite hypercube. We present two applications of our result; the first one deals with extremes of ggregate…

Let $\chi_n(t) = (\sum_{i=1}^n X_i^2(t))^{1/2},t\ge0$ be a chi-process with $n$ degrees of freedom where $X_i$'s are independent copies of some generic centered Gaussian process $X$. This paper derives the exact asymptotic behavior of…

In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear…

We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see…

To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…

In this paper, with motivation from [30] by Piterbarg (Extremes 7:161--177, 2004) and the considerable interest in stationary chi-processes, we derive asymptotic joint distributions of maxima of stationary strongly dependent chi-processes…

We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\beta$-Ensemble and prove its convergence to Poisson point process as $n\to +\infty$ when the inverse temperature…

Let $\{X(t) : t \in [0, \infty) \}$ be a centered stationary Gaussian process. We study the exact asymptotics of $\pr (\sup_{s \in [0,T]} X(t) > u)$, as $u \to \infty$, where $T$ is an independent of \{X(t)\} nonnegative random variable. It…

We investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct, where X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic processes. We assume that the process Y has subexponential characteristics and that the process…

Let $\{X(t),t\ge0\}$ be a centered Gaussian process and let $\gamma$ be a non-negative constant. In this paper we study the asymptotics of $P\{\underset{t\in [0,\mathcal{T}/u^\gamma]}\sup X(t)>u\}$ as $u\to\infty$, with $\mathcal{T}$ an…

In this contribution we are concerned with the asymptotic behaviour as $u\to \infty$ of $\mathbb{P}\{\sup_{t\in [0,T]} X_u(t)> u\}$, where $X_u(t),t\in [0,T],u>0$ is a family of centered Gaussian processes with continuous trajectories. A…