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

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 analy...

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Bibliographic Details
Main Author: Tudor, Ciprian
Format: eBook
Language:English
Published: Cham Springer International Publishing 2013, 2013
Edition:1st ed. 2013
Series:Probability and Its Applications
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Description
Summary: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 been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus
Physical Description:XI, 268 p online resource
ISBN:9783319009360