Parameter Estimation in Fractional Diffusion Models

• Main Authors: Kubilius, Kęstutis (Author), Mishura, Yuliya (Author), Ralchenko, Kostiantyn (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics, 8
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.

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 market...

Table of Contents:

• 1 Description and properties of the basic stochastic models
• 2 The Hurst index estimators for a fractional Brownian motion
• 3 Estimation of the Hurst index from the solution of a stochastic differential equation
• 4 Parameter estimation in the mixed models via power variations
• 5 Drift parameter estimation in diffusion and fractional diffusion models
• 6 The extended Orey index for Gaussian processes
• 7 Appendix A: Selected facts from mathematical and functional analysis
• 8 Appendix B: Selected facts from probability, stochastic processes and stochastic calculus.