Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion

  • Corinne Berzin
  • Alain Latour
  • José R. León
Part of the Lecture Notes in Statistics book series (LNS, volume 216)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Corinne Berzin, Alain Latour, José R. León
    Pages 1-28
  3. Corinne Berzin, Alain Latour, José R. León
    Pages 29-42
  4. Corinne Berzin, Alain Latour, José R. León
    Pages 43-58
  5. Corinne Berzin, Alain Latour, José R. León
    Pages 59-73
  6. Corinne Berzin, Alain Latour, José R. León
    Pages 75-107
  7. Corinne Berzin, Alain Latour, José R. León
    Pages 109-122
  8. Corinne Berzin, Alain Latour, José R. León
    Pages 123-158
  9. Corinne Berzin, Alain Latour, José R. León
    Pages 159-165
  10. Back Matter
    Pages 167-169

About this book

Introduction

This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered.

It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.

Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence.

The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events, and contaminant diffus

ion problems.

Keywords

Asymptotic properties of estimators Fractional Brownian motion Hypothesis testing Limit theorem Non parametric estimation Stochastic integral

Authors and affiliations

  • Corinne Berzin
    • 1
  • Alain Latour
    • 2
  • José R. León
    • 3
  1. 1.Laboratoire Jean-KuntzmannUniversité de Grenoble-AlpesGrenobleFrance
  2. 2.Laboratoire Jean-KuntzmannUniversité de Grenoble-AlpesGrenobleFrance
  3. 3.Escuela de Matemática, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-07875-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-07874-8
  • Online ISBN 978-3-319-07875-5
  • Series Print ISSN 0930-0325
  • Series Online ISSN 2197-7186
  • About this book