Related papers: Asymptotic tail behavior of phase-type scale mixtu…
We propose a new model and estimation framework for spatiotemporal streamflow exceedances above a threshold that flexibly captures asymptotic dependence and independence in the tail of the distribution. We model streamflow using a mixture…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index alpha<2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize…
The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic…
It is well known that waves propagating in a nontrivial medium develop ``tails''. However, the exact form of the late-time tail has so far been determined only for a narrow class of models. We present a systematic analysis of the tail…
In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
In this paper, we study the effects of correlated random phases in the intensity of a superposition of $N$ wave-fields. Our results suggest that regardless of whether the phase distribution is continuous or discrete if the phases are random…
To achieve a greater general flexibility for modeling heavy-tailed bounded responses, a beta scale mixture model is proposed. Each member of the family is obtained by multiplying the scale parameter of the conditional beta distribution by a…
The sums and maxima of weighted non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraints are that there exists a unique…
We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…
Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…
Consider a random walk $S=(S_n:n\geq 0)$ that is ``perturbed'' by a stationary sequence $(\xi_n:n\geq 0)$ to produce the process $(S_n+\xi_n:n\geq0)$. This paper is concerned with computing the distribution of the all-time maximum…
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…