Analysis of variations for self-similar processes : a stochastic calculus approach
著者
書誌事項
Analysis of variations for self-similar processes : a stochastic calculus approach
(Probability and its applications)
Springer, c2013
大学図書館所蔵 全14件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 259-266) and index
内容説明・目次
内容説明
Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises.
In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.
目次
Preface.- Introduction.- Part I Examples of Self-Similar Processes.- 1.Fractional Brownian Motion and Related Processes.- 2.Solutions to the Linear Stochastic Heat and Wave Equation.- 3.Non Gaussian Self-Similar Processes.- 4.Multiparameter Gaussian Processes.- Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems.- 5.First and Second Order Quadratic Variations. Wavelet-Type Variations.- 6.Hermite Variations for Self-Similar Processes.- Appendices: A.Self-Similar Processes with Stationary Increments: Basic Properties.- B.Kolmogorov Continuity Theorem.- C.Multiple Wiener Integrals and Malliavin Derivatives.- References.- Index.
「Nielsen BookData」 より