Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

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 serves as a standard reference, making this area accessible not only to
researchers in probability and statistics, but also to graduate students and practitioners. The …

Statistical Methods for Long Term Memory Processes covers the diverse statistical methods
and applications for data with long-range dependence. Presenting material that previously …

Stochastic Process Limits are useful and interesting because they generate simple
approximations for complicated stochastic processes and also help explain the statistical …

This comprehensive text gives an interesting and useful blend of the mathematical,
probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of …

A method of deriving asymptotics for linear processes is introduced which uses an explicit
algebraic decomposition of the linear filter. The technique is closely related to Gordin's …

We consider quantile autoregression (QAR) models in which the autoregressive coefficients
can be expressed as monotone functions of a single, scalar random variable. The models …

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 …