Rao Statistical Inference for Fractional Diffusion Processes

1. Auflage 2010
ISBN: 978-0-470-66713-2
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 280 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Stochastic processes are widely used for model building in thesocial, physical, engineering and life sciences as well as infinancial economics. In model building, statistical inference forstochastic processes is of great importance from both a theoreticaland an applications point of view.
This book deals with Fractional Diffusion Processes andstatistical inference for such stochastic processes. The main focusof the book is to consider parametric and nonparametric inferenceproblems for fractional diffusion processes when a complete path ofthe process over a finite interval is observable.
Key features:
* Introduces self-similar processes, fractional Brownian motionand stochastic integration with respect to fractional Brownianmotion.
* Provides a comprehensive review of statistical inference forprocesses driven by fractional Brownian motion for modelling longrange dependence.
* Presents a study of parametric and nonparametric inferenceproblems for the fractional diffusion process.
* Discusses the fractional Brownian sheet and infinitedimensional fractional Brownian motion.
* Includes recent results and developments in the area ofstatistical inference of fractional diffusion processes.
Researchers and students working on the statistics of fractionaldiffusion processes and applied mathematicians and statisticiansinvolved in stochastic process modelling will benefit from thisbook.

Autoren/Hrsg.

Rao, B. L. S. Prakasa

Inhaltsverzeichnis

Preface
1 Fractional Brownian Motion and Related Processes
1.1 Introduction
1.2 Self-similar processes
1.3 Fractional Brownian motion
1.4 Stochastic differential equations driven by fBm
1.5 Fractional Ornstein-Uhlenbeck type process
1.6 Mixed fractional Brownian motion
1.7 Donsker type approximation for fBm with Hurst index H >12
1.8 Simulation of fractional Brownian motion
1.9 Remarks on application of modelling by fBm in mathematicalfinance
1.10 Path wise integration with respect to fBm
2 Parametric Estimation for Fractional DiffusionProcesses
2.1 Introduction
2.2 Stochastic differential equations and local asymptoticnormality
2.3 Parameter estimation for linear SDE
2.4 Maximum likelihood estimation
2.5 Bayes estimation
2.6 Berry-Esseen type bound for MLE
2.7 _-upper and lower functions for MLE
2.8 Instrumental variable estimation
3 Parametric Estimation for Fractional Ornstein-UhlenbeckType Process
3.1 Introduction
3.2 Preliminaries
3.3 Maximum likelihood estimation
3.4 Bayes estimation
3.5 Probabilities of large deviations of MLE and BE
3.6 Minimum L1-norm estimation
4 Sequential Inference for Some Processes Driven byFractional Brownian
Motion
4.1 Introduction
4.2 Sequential maximum likelihood estimation
4.3 Sequential testing for simple hypothesis
5 Nonparametric Inference for Processes Driven by FractionalBrownian
Motion
5.1 Introduction
5.2 Identification for linear stochastic systems
5.3 Nonparametric estimation of trend
6 Parametric Inference for Some SDE's Driven byProcesses Related to
FBM
6.1 Introduction
6.2 Estimation of the the translation of a process driven by afBm
6.3 Parametric inference for SDE with delay governed by afBm
6.4 Parametric estimation for linear system of SDE driven byfBm's with different
Hurst indices
6.5 Parametric estimation for SDE driven by mixed fBm
6.6 Alternate approach for estimation in models driven byfBm
6.7 Maximum likelihood estimation under misspecified model
7 Parametric Estimation for Processes Driven by FractionalBrownian Sheet
7.1 Introduction
7.2 Parametric estimation for linear SDE driven by a fractionalBrownian sheet
8 Parametric Estimation for Processes Driven by InfiniteDimensional Fractional
Brownian Motion
8.1 Introduction
8.2 Parametric estimation for SPDE driven by infinitedimensional fBm
8.3 Parametric estimation for stochastic parabolic equationsdriven by infinite
dimensional fBm
9 Estimation of Self-Similarity Index
9.1 Introduction
9.2 Estimation of the Hurst index H when H is a constant and 12< H < 1 for fBm
9.3 Estimation of scaling exponent function H(.) for locallyself-similar processes
10 Filtering and Prediction for Linear Systems Driven byFractional Brownian
Motion
10.1 Introduction
10.2 Prediction of fractional Brownian motion
10.3 Filtering in a simple linear system driven by a fBm
10.4 General approach for filtering for linear systems driven byfBm
References
Index