Statistical Inference for Fractional Diffusion Processes (eBook)

B.L.S. Prakasa Rao, Department of Mathematics and Statistics, University of Hyderabad, India. Professor Rao is one of the world's foremost researchers in this complex area of probability theory.

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 mathematical
finance

1.10 Path wise integration with respect to fBm

2 Parametric Estimation for Fractional Diffusion
Processes

2.1 Introduction

2.2 Stochastic differential equations and local asymptotic
normality

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-Uhlenbeck
Type 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 by
Fractional 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 Fractional
Brownian

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 by
Processes Related to

FBM

6.1 Introduction

6.2 Estimation of the the translation of a process driven by a
fBm

6.3 Parametric inference for SDE with delay governed by a
fBm

6.4 Parametric estimation for linear system of SDE driven by
fBm's with different

Hurst indices

6.5 Parametric estimation for SDE driven by mixed fBm

6.6 Alternate approach for estimation in models driven by
fBm

6.7 Maximum likelihood estimation under misspecified model

7 Parametric Estimation for Processes Driven by Fractional
Brownian Sheet

7.1 Introduction

7.2 Parametric estimation for linear SDE driven by a fractional
Brownian sheet

8 Parametric Estimation for Processes Driven by Infinite
Dimensional Fractional

Brownian Motion

8.1 Introduction

8.2 Parametric estimation for SPDE driven by infinite
dimensional fBm

8.3 Parametric estimation for stochastic parabolic equations
driven 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 locally
self-similar processes

10 Filtering and Prediction for Linear Systems Driven by
Fractional 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 by
fBm

References

Index

"Provides a comprehensive review of statistical inference for
processes driven by fractional Brownian motion for modeling long
range dependence." (Bulletin Bibliographique, 2011)