Author 
Berzin, Corinne,

Series 
Lecture Notes in Statistics, 09300325 ; 216 

Lecture notes in statistics (SpringerVerlag) ;
216.

Subject 
Brownian motion processes.


Analysis of variance.

Alt Name 
Latour, Alain,


León, José Rafael,

Description 
1 online resource (xxviii, 169 pages) : illustrations (some color). 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
1. Introduction  2. Preliminaries  3. Estimation of the Parameters  4. Simulation Algorithms and Simulation Studies  5. Proofs of all the results  A. Complementary Results  A.1. Introduction  A.2. Proofs  B. Tables and Figures Related to the Simulation Studies  C. Some Pascal Procedures and Functions  References  Index. 

Machine generated contents note: 1. Introduction  1.1. Motivation  1.2. CLT for Nonlinear Functionals of Gaussian Processes  1.3. Main Result  1.4. Brownian Motion Increments  1.5. Other Increments of the Bm  1.6. Discretization  1.7. Crossings and Local Time for Smoothing fBm  References  2. Preliminaries  2.1. Introduction  2.2. Fractional Brownian Motion, Stochastic Integration and Complex Wiener Chaos  2.2.1. Preliminaries on Fractional Brownian Motion and Stochastic Integration  2.2.2. Complex Wiener Chaos  2.3. Hypothesis and Notation  References  3. Estimation of the Parameters  3.1. Introduction  3.2. Estimation of the Hurst Parameter  3.2.1. Almost Sure Convergence for the Second Order Increments  3.2.2. Convergence in Law of the Absolute kPower Variation  3.2.3. Estimators of the Hurst Parameter  3.3. Estimation of the Local Variance  3.3.1. Simultaneous Estimation of the Hurst Parameter and of the Local Variance  3.3.2. Hypothesis Testing  3.3.3. Functional Estimation of the Local Variance  References  4. Simulation Algorithms and Simulation Studies  4.1. Introduction  4.2. Computing Environment  4.3. Random Generators  4.4. Simulation of a Stationary Gaussian Process and of the fBm  4.5. Simulation Studies  4.5.1. Estimators of the Hurst Parameter and the Local Variance Based on the Observation of One Trajectory  4.5.2. Estimation of σ  4.5.3. Estimators of H and σ Based on the Observation of X(t)  4.5.4. Hypothesis Testing  References  5. Proofs of All the Results  5.1. Introduction  5.2. Estimation of the Hurst Parameter  5.2.1. Almost Sure Convergence for the Second Order Increments  5.2.2. Convergence in Law of the Absolute kPower Variation  5.2.3. Estimators of the Hurst Parameter  5.3. Estimation of the Local Variance  5.3.1. Simultaneous Estimators of the Hurst Parameter and of the Local Variance  5.3.2. Hypothesis Testing  5.3.3. Functional Estimation of the Local Variance  References  6. Complementary Results  6.1. Introduction  6.2. Proofs  7. Tables and Figures Related to the Simulation Studies  7.1. Introduction  8. Some Pascal Procedures and Functions. 
Summary 
This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the "Fourth Moment Theorem" is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence. The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling reallife events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events, and contaminant diffusion problems. 
Note 
Online resource; title from PDF title page (SpringerLink, viewed November 6, 2014). 
ISBN 
9783319078755 (electronic bk.) 

3319078755 (electronic bk.) 

3319078747 (print) 

9783319078748 (print) 

9783319078748 
ISBN/ISSN 
10.1007/9783319078755 
OCLC # 
894508399 
Additional Format 
Printed edition: 9783319078748 
