Stochastic Processes and Long Range Dependence. 1st ed. 2016

種類:

電子ブック

責任表示:

by Gennady Samorodnitsky

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2016

著者名:

• Samorodnitsky, Gennady.
• SpringerLink (Online service)

シリーズ名:

Springer Series in Operations Research and Financial Engineering ;

ISBN:

9783319455754 [3319455753]    

注記:

Preface -- Stationary Processes -- Ergodic Theory of Stationary Processes -- Infinitely Divisible Processes -- Heavy Tails -- Hurst Phenomenon -- Second-order Theory -- Fractionally Integrated Processes -- Self-similar Processes -- Long Range Dependence as a Phase Transition -- Appendix.
This monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been publishe

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