Probability and Its Applications

Analysis of Variations for Self-similar Processes

A Stochastic Calculus Approach

Authors: Tudor, Ciprian A.

  • Introduces new concepts
  • Surveys modern techniques and new results on limit theorems and stochastic calculus
  • Useful to probabilists and statisticians​
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About this book

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.  

About the authors

Ciprian Tudor is Full Professor at the University of Lille 1, France. He graduated from the University of Bucharest, Romania in 1998 and he obtained his PH.D. degree on Probability Theory from Université de La Rochelle, France in 2002. After the doctorate he worked at the Université Pierre et Marie Curie Paris 6, France and at the Université de Panthéon-Sorbonne Paris 1 where he obtained the Habilitation in 2006. He has published intensively on stochastic processes, especially Malliavin calculus, self-similar processes and their applications. Up to 2012 he has over 80 scientific publications in various international recognized journals on probability theory and statistics.

Reviews

“The author provides the general theory for different classes of self-similar processes with a complete treatment of limit theorems for their variations. … The book is self-contained and suitable for both graduate students with a basic background in probability theory and stochastic processes and researchers whose aim is investigating this topic.” (Anthony Réveillac, Mathematical Reviews, February, 2015)

“This monograph is a profound survey of recent developments in the fields of … self-similar processes and their calculus of variations. … It may serve as an excellent basis for research seminars or special classes on Gaussian processes and Malliavin’s calculus and as a starting point for applied mathematicians with interest in self-similar processes.” (Michael Högele, zbMATH 1308.60004, 2015)


Table of contents (6 chapters)

  • Fractional Brownian Motion and Related Processes

    Tudor, Ciprian A.

    Pages 3-25

  • Solutions to the Linear Stochastic Heat and Wave Equation

    Tudor, Ciprian A.

    Pages 27-75

  • Non-Gaussian Self-similar Processes

    Tudor, Ciprian A.

    Pages 77-101

  • Multiparameter Gaussian Processes

    Tudor, Ciprian A.

    Pages 103-117

  • First and Second Order Quadratic Variations. Wavelet-Type Variations

    Tudor, Ciprian A.

    Pages 121-204

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-00936-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-00935-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-319-03368-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Analysis of Variations for Self-similar Processes
Book Subtitle
A Stochastic Calculus Approach
Authors
Series Title
Probability and Its Applications
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00936-0
DOI
10.1007/978-3-319-00936-0
Hardcover ISBN
978-3-319-00935-3
Softcover ISBN
978-3-319-03368-6
Series ISSN
1431-7028
Edition Number
1
Number of Pages
XI, 268
Topics