Title Inference on the Hurst parameter and the variance of diffusions driven by fractional Brownian motion / Corinne Berzin, Alain Latour, José R. León

Published Cham : Springer, [2014] ©2014

Click on the following:
Springer Mathematics and Statistics eBooks
Springer eBooks

Copies

Description 1 online resource (xxviii, 169 pages) : illustrations (some color) Series Lecture Notes in Statistics, 0930-0325 ; 216 Lecture notes in statistics (Springer-Verlag) ; 216. Contents 880-01 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 880-01/(S Machine generated contents note: 1. Introduction -- 1.1. Motivation -- 1.2. CLT for Non-linear 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 k-Power 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 k-Power 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 real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events, and contaminant diffusion problems Analysis toegepaste statistiek applied statistics waarschijnlijkheidstheorie probability theory stochastische processen stochastic processes statistische analyse statistical analysis statistiek statistics simulatiemodellen simulation models economie economics Statistics (General) Statistiek (algemeen) Bibliography Includes bibliographical references and index Notes English Online resource; title from PDF title page (SpringerLink, viewed November 6, 2014) Subject Brownian motion processes. Analysis of variance. Analysis of Variance MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Analysis of variance Brownian motion processes Form Electronic book Author Latour, Alain, author León, José Rafael, author. ISBN 9783319078755 3319078755 3319078747 9783319078748

  Permalink