Related papers: On Rapid Variation of Multivariate Probability Den…
The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a…
The relativistic equilibrium velocity distribution coincides with the Maxwellian distribution for small velocities and vanishes at c, the velocity of light. Based on the decay pattern of high-energy tail in the relativistic equilibrium…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…
We present a simple model that accurately describes various statistical properties of peculiar velocities of dark matter halos. We pay particular attention to the following two effects; first, the evolution of the halo peculiar velocity…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
A random variable $\xi$ has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (\lambda \xi) <\infty$ for some $\lambda >0$, and has a {\it heavy-tailed} distribution (is…
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.
We study the fluctuations of a stochastic Maxwell-Lorentz particle model driven by an external field to determine the extent to which fluctuation relations are related to large deviations. Focusing on the total entropy production of this…
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…
Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before.…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
This note contains sufficient conditions for the probability density function of an arbitrary continuous univariate distribution, supported on $(0,\infty),$ such that the corresponding Mills ratio to be reciprocally convex (concave). To…
This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We…