Analysis of Variations for Self-similar Processes : A Stochastic Calculus Approach

種類:

電子ブック

責任表示:

by Ciprian Tudor

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2013

著者名:

• Tudor, Ciprian
• SpringerLink (Online service)

シリーズ名:

Probability and Its Applications ;

ISBN:

9783319009360 [3319009362]    

注記:

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 interrrelationship. 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

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