Bocconi & Springer Series

Selected Aspects of Fractional Brownian Motion

Authors: Nourdin, Ivan

  • Except for very few exception, every result stated in this book is proved in details: the book is then perfectly tailored for self-learning
  • My guiding thread was to develop only the most aesthetic topics related to fractional Brownian motion: the book will appeal to readers who are not necessarily familiar with fractional Brownian motion and who like beautiful mathematics
  • A special chapter on a recent link between fractional Brownian motion and free probability introduces the reader to a new and promising line of research
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  • ISBN 978-88-470-2823-4
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About this book

Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.

About the authors

Ivan Nourdin is full professor in Mathematics at Université de Lorraine (France). His research interests include Malliavin calculus, Stein's method and free probability.

Reviews

From the reviews:

“This short monograph by Ivan Nourdin deals with several aspects of fractional Brownian motion (fBm) ranging from basic properties over integration theory to non-commutative fractional Brownian motion. … The text is well written and almost all results are given with complete proofs. It is certainly a valuable contribution to the literature on fBm and will be a helpful source for everybody interested in new developments on fBm and its relation to other fields.” (Hilmar Mai, zbMATH, Vol. 1274, 2013)


Table of contents (8 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-88-470-2823-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-88-470-2822-7
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 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
Selected Aspects of Fractional Brownian Motion
Authors
Series Title
Bocconi & Springer Series
Copyright
2012
Publisher
Springer-Verlag Mailand
Copyright Holder
Springer-Verlag Italia
eBook ISBN
978-88-470-2823-4
DOI
10.1007/978-88-470-2823-4
Hardcover ISBN
978-88-470-2822-7
Series ISSN
2039-1471
Edition Number
1
Number of Pages
X, 122
Topics