Stochastic Models with Power-Law Tails

The Equation X = AX + B

Business & Finance, Economics, Statistics, Nonfiction, Science & Nature, Mathematics
Cover of the book Stochastic Models with Power-Law Tails by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Dariusz Buraczewski, Ewa Damek, Thomas Mikosch ISBN: 9783319296791
Publisher: Springer International Publishing Publication: July 4, 2016
Imprint: Springer Language: English
Author: Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
ISBN: 9783319296791
Publisher: Springer International Publishing
Publication: July 4, 2016
Imprint: Springer
Language: English

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems.

The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems.

The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.

More books from Springer International Publishing

Cover of the book Micromechanics of Materials, with Applications by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book The Role of Twitter in the 2016 US Election by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Hegel and Empire by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Applications of Topological Methods in Molecular Chemistry by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Nonlinear Elliptic Partial Differential Equations by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Informatics in Control, Automation and Robotics by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Flood Risk in the Upper Vistula Basin by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Problems of Normativity, Rules and Rule-Following by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Polarization, Alignment, and Orientation in Atomic Collisions by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book The Poetics of Space and Place in Scottish Literature by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Power System Optimization Modeling in GAMS by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Wireless Virtualization by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Digital Health by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Geoenergy Modeling I by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Cover of the book Health, Technologies, and Politics in Post-Soviet Settings by Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy