Related papers: Exponential exact estimation for maximum and minim…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
In this paper, joint asymptotics of powered maxima for a triangular array of bivariate powered Gaussian random vectors are considered. Under the H\"usler-Reiss condition, limiting distributions of powered maxima are derived. Furthermore,…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
We derive the exponential non improvable Grand Lebesgue Space norm decreasing estimations for tail of distribution for exact normed deviation for the famous recursive Wolverton-Wagner multivariate statistical density estimation. We consider…
This article concerns the non-asymptotic analysis of the singular values (and Lyapunov exponents) of Gaussian matrix products in the regime where $N,$ the number of term in the product, is large and $n,$ the size of the matrices, may be…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale and martingale transform by means of martingale differences in the terms of moments and tails of distributions…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P(X > x, Y> y) for x,y…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
We propose a novel mechanism for the origin of non-Gaussian tails in the probability distribution functions (PDFs) of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields.…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
We derive exact asymptotics of $$\mathbb{P}\left(\sup_{\mathbf{t}\in {\mathcal{A}}}X(\mathbf{t})>u\right),~ \text{as}~ u\to\infty,$$ for a centered Gaussian field $X(\mathbf{t}),~ \mathbf{t}\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
We consider the sums $S_n=\xi_1+\cdots+\xi_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the…
We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…