Related papers: The tail process revisited
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
A class of stochastic processes strongly related to random sums plays an important role in network and in finance. In this paper we study this kind of stochastic process discuss an overtime unchanged parameter and reveal its asymptotic…
Many tasks are accomplished via random processes. The completion time of such a task can be profoundly affected by restart: the occasional resetting of the task's underlying random process. Consequently, determining when restart will impede…
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…
This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…
The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a…
Time series analysis is relevant in various disciplines such as physics, biology, chemistry, and finance. In this paper, we present a novel neural network architecture that integrates elements from ResNet structures, while introducing the…
The areas under workload process and under queuing process in a single server queue over the busy period have many applications not only in queuing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
In order to capture the dependence in the upper tail of a time series, we develop non-negative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…
Temporal information conveyed by language describes how the world around us changes through time. Events, durations and times are all temporal elements that can be viewed as intervals. These intervals are sometimes temporally related in…
A new approach is developed to understand stability of a population and further understanding of population momentum.
A scan statistic is examined for the purpose of testing the existence of a global peak in a random process with dependent variables of any distribution. The scan statistic tail probability is obtained based on the covariance of the moving…
We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…
This paper considers one-dimensional mixed causal/noncausal autoregressive (MAR) processes with heavy tail, usually introduced to model trajectories with patterns including asymmetric peaks and throughs, speculative bubbles, flash crashes,…
In this paper, we consider the state-dependent reflecting random walk on a half-strip. We provide explicit criteria for (positive) recurrence, and an explicit expression for the stationary distribution. As a consequence, the light-tailed…