Statistical inference for fractional diffusion processes

✍ Scribed by B. L. S. Prakasa Rao

• Publisher: Wiley
• Year: 2010
• Tongue: English
• Leaves: 277
• Series: Wiley Series in Probability and Statistics
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Title Page......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1.1 Introduction......Page 15
1.2 Self-similar processes......Page 16
1.3 Fractional Brownian motion......Page 21
1.4 Stochastic differential equations driven by fBm......Page 38
1.5 Fractional Ornstein–Uhlenbeck-type process......Page 44
1.6 Mixed fBm......Page 47
1.7 Donsker-type approximation for fBm with Hurst index H > 1/2......Page 49
1.8 Simulation of fBm......Page 50
1.10 Pathwise integration with respect to fBm......Page 53
2.2 SDEs and local asymptotic normality......Page 59
2.3 Parameter estimation for linear SDEs......Page 61
2.4 Maximum likelihood estimation......Page 62
2.5 Bayes estimation......Page 65
2.6 Berry–Esseen-type bound for MLE......Page 72
2.7 [Omitted]-upper and lower functions for MLE......Page 74
2.8 Instrumental variable estimation......Page 83
3.1 Introduction......Page 91
3.2 Preliminaries......Page 92
3.3 Maximum likelihood estimation......Page 93
3.4 Bayes estimation......Page 97
3.5 Probabilities of large deviations of MLE and BE......Page 98
3.6 Minimum L1-norm estimation......Page 107
4.2 Sequential maximum likelihood estimation......Page 115
4.3 Sequential testing for simple hypothesis......Page 119
5.2 Identification for linear stochastic systems......Page 129
5.3 Nonparametric estimation of trend......Page 144
6.2 Estimation of the translation of a process driven by fBm......Page 157
6.3 Parametric inference for SDEs with delay governed by fBm......Page 170
6.4 Parametric estimation for linear system of SDEs driven by fBms with different Hurst indices......Page 177
6.5 Parametric estimation for SDEs driven by mixed fBm......Page 187
6.6 Alternate approach for estimation in models driven by fBm......Page 195
6.7 Maximum likelihood estimation under misspecified model......Page 198
7.2 Parametric estimation for linear SDEs driven by a fractional Brownian sheet......Page 203
8.2 Parametric estimation for SPDEs driven by infinite-dimensional fBm......Page 219
8.3 Parametric estimation for stochastic parabolic equations driven by infinite-dimensional fBm......Page 227
9.1 Introduction......Page 233
9.2 Estimation of the Hurst index H when H is a constant and 1/2 < H < 1 for fBm......Page 234
9.3 Estimation of scaling exponent function H(.) for locally self-similar processes......Page 239
10.2 Prediction of fBm......Page 243
10.3 Filtering in a simple linear system driven by fBm......Page 244
10.4 General approach for filtering for linear systems driven by fBms......Page 246
References......Page 253
Index......Page 265