Prakasa Rao B.L.S. Statistical Inference for Fractional Diffusion Processes

Hoboken: Wiley, 2010. — 277 p.Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view.This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable.Key features:Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion.Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence.Presents a study of parametric and nonparametric inference problems for the fractional diffusion process.Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion.Includes recent results and developments in the area of statistical inference of fractional diffusion processes.Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.Self-similar processes
Fractional Brownian motion
Stochastic differential equations driven by fBm
Fractional Ornstein–Uhlenbeck-type process
Mixed fBm
Donsker-type approximation for fBm with Hurst index H > /
Simulation of fBm
Pathwise integration with respect to fBm
SDEs and local asymptotic normality
Parameter estimation for linear SDEs
Maximum likelihood estimation
Bayes estimation
Berry–Esseen-type bound for MLE
[Omitted]-upper and lower functions for MLE
Instrumental variable estimationPreliminaries
Maximum likelihood estimation
Bayes estimation
Probabilities of large deviations of MLE and BE
Minimum L-norm estimation
Sequential maximum likelihood estimation
Sequential testing for simple hypothesis
Identification for linear stochastic systems
Nonparametric estimation of trend
Estimation of the translation of a process driven by fBm
Parametric inference for SDEs with delay governed by fBm
Parametric estimation for linear system of SDEs driven by fBms with different Hurst indices
Parametric estimation for SDEs driven by mixed fBm
Alternate approach for estimation in models driven by fBm
Maximum likelihood estimation under misspecified model
Parametric estimation for linear SDEs driven by a fractional Brownian sheet
Parametric estimation for SPDEs driven by infinite-dimensional fBm
Parametric estimation for stochastic parabolic equations driven by infinite-dimensional fBmEstimation of the Hurst index H when H is a constant and / < H < for fBm
Estimation of scaling exponent function H() for locally self-similar processes
Prediction of fBm
Filtering in a simple linear system driven by fBm
General approach for filtering for linear systems driven by fBms