Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

Dariusz Buraczewski Ewa Damek Thomas Mikosch The Equation X = AX + B Page 1
Springer Series in Operations Research and Financial Engineering Dariusz Buraczewski …

This book is concerned with extreme value theory for stochastic processes whose finite-
dimensional distributions are heavy-tailed in the restrictive sense of regular variation. These …

I first heard about long-range dependence while working on a book on stable processes
with Murad Taqqu. Initially, the notion did not seem to stand out among other notions I was …

The asymptotic theory for the sample autocorrelations and extremes of a GARCH (1, 1)
process is provided. Special attention is given to the case when the sum of the ARCH and …

We consider a strictly stationary sequence of random vectors whose finite-dimensional
distributions are jointly regularly varying with some positive index. This class of processes …

Because of its potential to... predict the unpredictable,... extreme value theory (EVT) and
methodology is currently receiving a great deal of attention from statistical and mathematical …

Extreme values of a stationary, multivariate time series may exhibit dependence across
coordinates and over time. The aim of this paper is to offer a new and potentially useful tool …

First we give a short review of large deviation results for sums of iid random variables. The
main emphasis is on heavy-tailed distributions. We stress more the methodology than the …

We study the sample ACVF and ACF of a general stationary sequence under a weak mixing
condition and in the case that the marginal distributions are regularly varying. This includes …