In most species, the capability of perceiving and using the passage of time in the seconds-to-
minutes range (interval timing) is not only accurate but also scalar: errors in time estimation …

In this paper, we extend the remarkable M-estimator of Catoni\citep {Cat12} to situations
where the variance is infinite. In particular, given a sequence of iid random variables $\{X_i\} …

We study the estimation of a stable Cox–Ingersoll–Ross model, which is a special subcritical
continuous-state branching process with immigration. The exponential ergodicity and strong …

Levy noise can help neurons detect faint or subthreshold signals. Levy noise extends
standard Brownian noise to many types of impulsive jump-noise processes found in real and …

Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural
Networks (DNNs), including both production quality, pre-trained models such as AlexNet …

In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed
behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic …

The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

This book covers some of the main aspects of insurance mathematics, parts of risk
management and financial risk, and some relevant probabilistic tools. The view is theoretical …

This article investigates the tail asymptotic behavior of the sum of pairwise quasi-
asymptotically independent random variables with consistently varying tails. We prove that …

For the purpose of risk management, the study of tail behavior of multiple risks is more
relevant than the study of their overall distributions. Asymptotic study assuming that each …