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 …

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 …

The present book is dedicated to the late w. Leimbacher. It is based on lecture notes which
were written between 1975 and 1985 when I taught Non-Life Mathematics at the University …

We consider some elementary functions of the components of a regularly varying random
vector such as linear combinations, products, minima, maxima, order statistics, powers. We …

A univariate Hawkes process is a simple point process that is self-exciting and has a
clustering effect. The intensity of this point process is given by the sum of a baseline intensity …

ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories,
applications, and statistical methodologies essential to heavy tailed risk modeling Focusing …

We study conditions under which PS τ> x∼ PM τ> x∼ EτP ξ₁> x as x→∞, where S τ is a
sum ξ₁+···+ ξ τ of random size τ and M τ is a maximum of partial sums M τ= max n≤ τ S n …

The tail of the distribution of a sum of a random number of independent and identically
distributed nonnegative random variables depends on the tails of the number of terms and of …

A random vector X with representation X=∑_j≥0A_jZ_j is considered. Here, (Z_j) is a
sequence of independent and identically distributed random vectors and (A_j) is a sequence …

We study non-stationary random length sequences of random variables with regularly
varying tails. Tail and extremal indexes of their maxima and linear combinations are found …