Tempered Stable Distributions:Stochastic Models for Multiscale Processes SpringerBriefs in Mathematics. 1st ed. 2016 Michael Grabchak
Tempered Stable Distributions:Stochastic Models for Multiscale Processes. 1st ed. 2015 Michael Grabchak, Michael Grabchak
This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
Principles of Stable Isotope Distribution: Robert E. Criss
Refined Bootstrap for Stable Paretian Distributions:with Applications to Financial Returns Adriana Cornea
Tempered Stable Distributions ab 39.99 EURO Stochastic Models for Multiscale Processes SpringerBriefs in Mathematics. 1st ed. 2016
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics - such as the classical central limit theorem - which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the masters level with a solid knowledge of measure theoretic probability. Erich Haeusler studied mathematics and physics at the University of Bochum from 1972 to 1978. He received his doctorate in mathematics in 1982 from the University of Munich. Since 1991 he has been Professor of Mathematics at the University of Giessen, where he teaches probability and mathematical statistics. Harald Luschgy studied mathematics, physics and mathematical logic at the Universities of Bonn and Münster. He received his doctorate in mathematics in 1976 from the University of Münster. He held visiting positions at the Universities of Hamburg, Bayreuth, Dortmund, Oldenburg, Passau and Wien and was a recipient of a Heisenberg grant from the DFG. Since 1995 he is Professor of Mathematics at the University of Trier where he teaches probability and mathematical statistics.
This book provides a self-contained presentation on the structure of a large class of stable processes, known as self-similar mixed moving averages. The authors present a way to describe and classify these processes by relating them to so-called deterministic flows. The first sections in the book review random variables, stochastic processes, and integrals, moving on to rigidity and flows, and finally ending with mixed moving averages and self-similarity. In-depth appendices are also included. This book is aimed at graduate students and researchers working in probability theory and statistics. Vladas Pipiras is Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. His main research interests focus on stochastic processes exhibiting long-range dependence, self-similarity and other scaling phenomena, as well as on stable, extreme-value and other distributions possessing heavy tails. His other current interests include high-dimensional time series, sampling issues for big data and stochastic dynamical systems, with applications in Econometrics, Neuroscience, Engineering, Computer Science and other areas. Vladas Pipiras has written over 50 research papers, and is a coauthor of a graduate textbook on measure theory and probability. Murad S. Taqqus research involves self-similar processes, their connection to time series with long-range dependence , the development of statistical tests, and the study of non-Gaussian processes whose marginal distributions have heavy tails. He has written more than 250 scientific papers and is the coauthor of a standard reference on stable non-Gaussian random processes. Professor Taqqu is a Fellow of the Institute of Mathematical Statistics and has been elected Member of the International Statistical Institute. He has received a number of awards, including a John Simon Guggenheim Fellowship, the 1995 William J. Bennett Award, the 1996 IEEE W.R.G. Baker Prize, the 2002 EURASIO Best Paper Award and the 2006 ACM/SIGCOMM Test of Time Award.
Chance and Stability:Stable Distributions and their Applications. Reprint 2011 Vladimir V. Uchaikin, Vladimir M. Zolotarev