Statistical Inference for Fractional Diffusion Processes

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