Selected Aspects of Fractional Brownian Motion

  • Ivan Nourdin

Part of the B&SS — Bocconi & Springer Series book series (BS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Ivan Nourdin
    Pages 1-10
  3. Ivan Nourdin
    Pages 11-22
  4. Ivan Nourdin
    Pages 53-64
  5. Ivan Nourdin
    Pages 103-116
  6. Back Matter
    Pages 117-124

About this book

Introduction

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.

Keywords

Fractional Brownian motion Integration Limit theorems Malliavin calculus Maximum of Gaussian processes

Authors and affiliations

  • Ivan Nourdin
    • 1
  1. 1.Université de LorraineVandoeuvre-lès-NancyFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-88-470-2823-4
  • Copyright Information Springer-Verlag Italia 2012
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-88-470-2822-7
  • Online ISBN 978-88-470-2823-4
  • Series Print ISSN 2039-1471
  • Series Online ISSN 2039-148X
  • About this book