國立虎尾科技大學 |

Stochastic Processes and Long Range Dependence

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic Processes and Long Range Dependence/ by Gennady Samorodnitsky.
Author:	Samorodnitsky, Gennady.
Description:	XI, 415 p. 5 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-3-319-45575-4
ISBN:	9783319455754

Stochastic Processes and Long Range Dependence
Samorodnitsky, Gennady.

Stochastic Processes and Long Range Dependence[electronic resource] /by Gennady Samorodnitsky. - 1st ed. 2016. - XI, 415 p. 5 illus.online resource. - Springer Series in Operations Research and Financial Engineering,1431-8598. - Springer Series in Operations Research and Financial Engineering,.

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 published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.

ISBN: 9783319455754

Standard No.: 10.1007/978-3-319-45575-4doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Stochastic Processes and Long Range Dependence
LDR:03172nam a22004335i 4500 001 971948
003 DE-He213
005 20200703145050.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319455754 $9 978-3-319-45575-4
024 7 $a 10.1007/978-3-319-45575-4 $2 doi
035 $a 978-3-319-45575-4
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Samorodnitsky, Gennady. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115828
245 1 0 $a Stochastic Processes and Long Range Dependence $h [electronic resource] / $c by Gennady Samorodnitsky.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a XI, 415 p. 5 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Series in Operations Research and Financial Engineering, $x 1431-8598
505 0 $a 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.
520 $a 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 published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.
650 0 $a Probabilities. $3 527847
650 0 $a Measure theory. $3 527848
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319455747
776 0 8 $i Printed edition: $z 9783319455761
776 0 8 $i Printed edition: $z 9783319833217
830 0 $a Springer Series in Operations Research and Financial Engineering, $x 1431-8598 $3 1267183
856 4 0 $u https://doi.org/10.1007/978-3-319-45575-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)