Related papers: Hoeffding-Style Concentration Bounds for Exchangea…

We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…

We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with heavy tail of maximum distribution.

We consider a multivariate distributional recursion of sum-type as arising in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the…

We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…

In this paper we study the long time-long range behavior of reaction diffusion equations with negative square root -type reaction terms. In particular we investigate the exponential behavior of the solutions after a standard hyperbolic…

We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…

For the directed edge preferential attachment network growth model studied by Bollobas et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of in-degree and out-degree has jointly regularly varying tails.…

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are…

This note gives a proof of an improved upper bound for the right-side tail of a distribution discussed in "Crossover Distributions at the Edge of the Rarefaction Fan" by Ivan Corwin and Jeremy Quastel.

Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise 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.…

We establish concentration inequalities for Lipschitz functions of dependent random variables, whose dependencies are specified by forests. We also give concentration results for decomposable functions, improving Janson's Hoeffding-type…

Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…

Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these…

We present an upper bound on the mixing rate of the equilibrium state of a dynamical systems defined by the one-sided shift and a non H\"{o}lder potential of summable variations. The bound follows from an estimation of the relaxation speed…

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…

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…

Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable…