Statistical inference for fractional diffusion processes - Info and Reading Options

"Statistical inference for fractional diffusion processes" Table Of Contents:

• 1- Preface
• 2- 1 Fractional Brownian Motion and Related Processes
• 3- 1.1 Introduction
• 4- 1.2 Self-similar processes
• 5- 1.3 Fractional Brownian motion
• 6- 1.4 Stochastic differential equations driven by fBm
• 7- 1.5 Fractional Ornstein-Uhlenbeck type process
• 8- 1.6 Mixed fractional Brownian motion
• 9- 1.7 Donsker type approximation for fBm with Hurst index H >
• 10- 1.8 Simulation of fractional Brownian motion
• 11- 1.9 Remarks on application of modelling by fBm in mathematical finance
• 12- 1.10 Path wise integration with respect to fBm
• 13- 2 Parametric Estimation for Fractional Diffusion Processes
• 14- 2.1 Introduction
• 15- 2.2 Stochastic differential equations and local asymptotic normality
• 16- 2.3 Parameter estimation for linear SDE
• 17- 2.4 Maximum likelihood estimation
• 18- 2.5 Bayes estimation
• 19- 2.6 Berry-Esseen type bound for MLE
• 20- 2.7-upper and lower functions for MLE
• 21- 2.8 Instrumental variable estimation
• 22- 3 Parametric Estimation for Fractional Ornstein-Uhlenbeck Type Process
• 23- 3.1 Introduction
• 24- 3.2 Preliminaries
• 25- 3.3 Maximum likelihood estimation
• 26- 3.4 Bayes estimation
• 27- 3.5 Probabilities of large deviations of MLE and BE
• 28- 3.6 Minimum L1-norm estimation
• 29- 4 Sequential Inference for Some Processes Driven by Fractional Brownian
• 30- Motion
• 31- 4.1 Introduction
• 32- 4.2 Sequential maximum likelihood estimation
• 33- 4.3 Sequential testing for simple hypothesis
• 34- 5 Nonparametric Inference for Processes Driven by Fractional Brownian
• 35- Motion
• 36- 5.1 Introduction
• 37- 5.2 Identification for linear stochastic systems
• 38- 5.3 Nonparametric estimation of trend
• 39- 6 Parametric Inference for Some SDE's Driven by Processes Related to FBM
• 40- 6.1 Introduction
• 41- 6.2 Estimation of the the translation of a process driven by a fBm
• 42- 6.3 Parametric inference for SDE with delay governed by a fBm
• 43- 6.4 Parametric estimation for linear system of SDE driven by fBm's with different Hurst indices
• 44- 6.5 Parametric estimation for SDE driven by mixed fBm
• 45- 6.6 Alternate approach for estimation in models driven by fBm
• 46- 6.7 Maximum likelihood estimation under misspecified model
• 47- 7 Parametric Estimation for Processes Driven by Fractional Brownian Sheet
• 48- 7.1 Introduction
• 49- 7.2 Parametric estimation for linear SDE driven by a fractional Brownian sheet
• 50- 8 Parametric Estimation for Processes Driven by Infinite Dimensional Fractional
• 51- Brownian Motion
• 52- 8.1 Introduction
• 53- 8.2 Parametric estimation for SPDE driven by infinite dimensional fBm
• 54- 8.3 Parametric estimation for stochastic parabolic equations driven by infinite dimensional fBm
• 55- 9 Estimation of Self-Similarity Index
• 56- 9.1 Introduction
• 57- 9.2 Estimation of the Hurst index H when H is a constant and 12 < H < 1 for fBm
• 58- 9.3 Estimation of scaling exponent function H(.) for locally self-similar processes
• 59- 10 Filtering and Prediction for Linear Systems Driven by Fractional Brownian
• 60- Motion
• 61- 10.1 Introduction
• 62- 10.2 Prediction of fractional Brownian motion
• 63- 10.3 Filtering in a simple linear system driven by a fBm
• 64- 10.4 General approach for filtering for linear systems driven by fBm References
• 65- Index

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