Related papers: Precise large deviations for dependent subexponent…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to…
We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so.…
We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
For a multivariate normal distribution, the sparsity of the covariance and precision matrices encodes complete information about independence and conditional independence properties. For general distributions, the covariance and precision…
We analyze the largest eigenvalue statistics of m-dependent heavy-tailed Wigner matrices as well as the associated sample covariance matrices having entry-wise regularly varying tail distributions with parameter $0<\alpha<4$. Our analysis…
This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…