相关论文: Tail behavior of solutions of linear recursions on…
Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions…
In this paper, we give a Breiman's theorem for conditional dependent random vector, where one component has a regularly-varying-tailed distribution with the index $\alpha\ge0$ and its slowly varying function satisfies a relaxed condition,…
We provide a new characterisation of Duquesne and Le Gall's $\alpha$-stable tree, $\alpha\in(1,2]$, as the solution of a recursive distribution equation (RDE) of the form $\mathcal{T}\overset{d}{=}g(\xi,\mathcal{T}_i, i\geq0)$, where $g$ is…
We analyze neural scaling laws in a solvable model of last-layer fine-tuning where targets have intrinsic, instance-heterogeneous difficulty. In our Latent Instance Difficulty (LID) model, each input's target variance is governed by a…
In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The…
Let $\{X_1, X_2, ... \}$ be a sequence of dependent heavy-tailed random variables with distributions $F_1, F_2,...$ on $(-\infty,\infty)$, and let $\tau$ be a nonnegative integer-valued random variable independent of the sequence $\{X_k, k…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
The sums and maxima of non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraint is that there exists a unique series in a…
This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…
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…
In this paper, we discuss the large--time behavior of solution of a simple kinetic model of Boltzmann--Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the…
Consider a random vector $U$, whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $U$, conditional on one of its components, has under a mild…
The upper tail problem in the Erd\H{o}s--R\'enyi random graph $G\sim\mathcal{G}_{n,p}$ asks to estimate the probability that the number of copies of a graph $H$ in $G$ exceeds its expectation by a factor $1+\delta$. Chatterjee and Dembo…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…
Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…
Assessing and managing risks in a changing climate requires projections that account for decision-relevant uncertainties. These deep uncertainties are often approximated by ensembles of Earth-system model runs that sample only a subset of…
I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…