Statistical issues arising in modelling univariate extremes of a random sample have been
successfully used in the most diverse fields, such as biometrics, finance, insurance and risk …

Publisher Summary This chapter focuses on the inequalities, small ball probabilities, and
application of Gaussian processes. It is well-known that the large deviation result plays a …

Almost a century ago, Lévy (1925) first explored stable distributions in his study of sums of
random terms. The basic mathematical facts about stable laws were described in the …

Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

Dependence Modeling with Copulas covers the substantial advances that have taken place
in the field during the last 15 years, including vine copula modeling of high-dimensional …

The monograph investigates the misapplication of conventional statistical techniques to fat
tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat …

The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions
in real-world networks. We first provide a rigorous definition of power-law distributions …

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 …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …