Related papers: Regular variation and free regular infinitely divi…

We consider an infinitely divisible random field indexed by $\mathbb{R}^d$, $d\in\mathbb{N}$, given as an integral of a kernel function with respect to a L\'evy basis with a L\'evy measure having a regularly varying right tail. First we…

An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…

We construct a random matrix model for the bijection \Psi between clas- sical and free infinitely divisible distributions: for every d\geq1, we associate in a quite natural way to each *-infinitely divisible distribution \mu a distribution…

In a 1999 paper, Bercovici and Pata showed that a natural bijection between the classically, free and Boolean infinitely divisible measures held at the level of limit theorems of triangular arrays. This result was extended to include…

In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…

In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard $p$-values, (c) respects frequentist…

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of…

We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating question has been whether a freely stable random matrix has…

We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is…

Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…

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…

Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…

The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…

We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite…

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…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The…

We study the behavior of the tail of a measure $\mu^{\boxtimes t}$, where $\boxtimes t$ is the $t$-fold free multiplicative convolution power for $t\geq 1$. We focus on the case where $\mu$ is a probability measure on the positive half-line…

We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework…