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Analysis of Variations for Self-similar Processes

A Stochastic Calculus Approach

  • Ciprian Tudor

Part of the Probability and Its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Examples of Self-similar Processes

    1. Front Matter
      Pages 1-1
    2. Ciprian A. Tudor
      Pages 77-101
    3. Ciprian A. Tudor
      Pages 103-117
  3. Variations of Self-similar Processes: Central and Non-Central Limit Theorems

    1. Front Matter
      Pages 119-119
    2. Ciprian A. Tudor
      Pages 205-249
  4. Back Matter
    Pages 251-268

About this book

Introduction

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.

Keywords

60F05, 60H05, 60G18 Malliavin calculus limit theorems self-similar stochastic processes stochastic equations variations of stochastic processes

Authors and affiliations

  • Ciprian Tudor
    • 1
  1. 1.Université de Lille 1 UFR MathématiquesVilleneuve d’AscqFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-00936-0
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-00935-3
  • Online ISBN 978-3-319-00936-0
  • Series Print ISSN 1431-7028
  • Buy this book on publisher's site