Related papers: On Sums of Conditionally Independent Subexponentia…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…
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…
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.…
Let $\xi_1, \xi_2,\ldots$ be a sequence of independent and identically distributed random variables with zero mean, finite second moment and regularly varying right distribution tail. Motivated by a stop-loss insurance model, we consider a…
Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$.…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with…
The class of subweibull distributions has recently been shown to generalize the important properties of subexponential and subgaussian random variables. We describe alternative characterizations of subweibull distributions and detail the…
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…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ and a sequence of i.i.d. $X$-valued random variables $\xi_1,\dots,\xi_n$, and give a good estimate on the tail behaviour of $\sup\limits_{f\in\Cal…
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov.…