Related papers: The tail process and tail measure of continuous ti…
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.
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such…
An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…
The extremal tail probabilities of moving sums in a marked Poisson random field is examined here. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. Change of measure…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
We look at joint regular variation properties of MA($\infty$) processes of the form $\mathbf{X} = (X_k, k \in \mathbb{Z})$ where $X_k = \sum_{j=0}^{\infty} \psi_j Z_{k-j}$ and the sequence of random variables $(Z_i, i \in \mathbb{Z})$ are…
We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established…
This article characterizes topological duals of spaces of cadlag processes. We obtain extensions of functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis. In particular, we obtain…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail…