Parameter Estimation in Fractional Diffusion Models

  • Kęstutis Kubilius
  • Yuliya Mishura
  • Kostiantyn Ralchenko

Part of the Bocconi & Springer Series book series (BS, volume 8)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 1-43
  3. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 45-74
  4. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 75-123
  5. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 125-160
  6. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 161-267
  7. Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko
    Pages 269-320
  8. Back Matter
    Pages 321-390

About this book

Introduction

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. 

The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Keywords

Fractional Brownian motion Diffusion model with memory Parameter estimation Orey index Hurst parameter

Authors and affiliations

  • Kęstutis Kubilius
    • 1
  • Yuliya Mishura
    • 2
  • Kostiantyn Ralchenko
    • 3
  1. 1.Institute of Data Science and Digital TechnologiesVilnius UniversityVilniusLithuania
  2. 2.Department of Probability Theory, Statistics and Actuarial MathematicsTaras Shevchenko National University of KyivKyivUkraine
  3. 3.Department of Probability Theory, Statistics and Actuarial MathematicsTaras Shevchenko National University of KyivKyivLithuania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-71030-3
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-71029-7
  • Online ISBN 978-3-319-71030-3
  • Series Print ISSN 2039-1471
  • Series Online ISSN 2039-148X
  • About this book
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