Bocconi & Springer Series

Parameter Estimation in Fractional Diffusion Models

Authors: Kubilius, Kęstutis, Mishura, Yuliya, Ralchenko, Kostiantyn

  • Presents a variety of diffusion models with memory
  • Offers methods of parameter estimation in the diffusion models with memory at the algorithmic level
  • Provides the results of computer simulations and compare the methods
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eBook 91,62 €
price for Spain (gross)
  • ISBN 978-3-319-71030-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-319-71029-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

Prof. Kęstutis Kubilius received his Ph.D. in mathematics at Vilnius University in 1981. Currently he is a professor of mathematics at the same university. His research work mainly focuses on limit theorems for semimartingales, theory of stochastic differential equations, and parameter estimation for fractional diffusion processes. He is the  author of more than 50 published papers.

Prof. Yuliya Mishura received her Ph.D. in probability and statistics at Kyiv University in 1978 and received her postdoctoral degree in probability and statistics (habilitation) in 1990. She is currently a professor at Taras Shevchenko National University of Kyiv. She is the author of more than 250 research papers and 6 books. Her  research interests include theory and statistics of stochastic processes, fractional processes, stochastic analysis and financial mathematics.

Dr. Kostiantyn Ralchenko is a postdoctoral researcher at the Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, where he also completed his Ph.D. in mathematics in 2012. His research interests include stochastic differential equations, fractional and multifractional processes, and statistics of stochastic processes. He is the author of 24 papers.

Table of contents (6 chapters)

  • Description and Properties of the Basic Stochastic Models

    Kubilius, Kęstutis (et al.)

    Pages 1-43

    Preview Buy Chapter 30,19 €
  • The Hurst Index Estimators for a Fractional Brownian Motion

    Kubilius, Kęstutis (et al.)

    Pages 45-74

    Preview Buy Chapter 30,19 €
  • Estimation of the Hurst Index from the Solution of a Stochastic Differential Equation

    Kubilius, Kęstutis (et al.)

    Pages 75-123

    Preview Buy Chapter 30,19 €
  • Parameter Estimation in the Mixed Models via Power Variations

    Kubilius, Kęstutis (et al.)

    Pages 125-160

    Preview Buy Chapter 30,19 €
  • Drift Parameter Estimation in Diffusion and Fractional Diffusion Models

    Kubilius, Kęstutis (et al.)

    Pages 161-267

    Preview Buy Chapter 30,19 €

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-3-319-71030-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-319-71029-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Parameter Estimation in Fractional Diffusion Models
Authors
Series Title
Bocconi & Springer Series
Series Volume
8
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-71030-3
DOI
10.1007/978-3-319-71030-3
Hardcover ISBN
978-3-319-71029-7
Series ISSN
2039-1471
Edition Number
1
Number of Pages
XIX, 390
Number of Illustrations and Tables
15 b/w illustrations, 2 illustrations in colour
Topics