Statistical inference for fractional diffusion processes
Preface -- 1 Fractional Brownian Motion and Related Processes -- 1.1 Introduction -- 1.2 Self-similar processes -- 1.3 Fractional Brownian motion -- 1.4 Stochastic differential equations driven by fBm -- 1.5 Fractional Ornstein-Uhlenbeck type process -- 1.6 Mixed fractional Brownian motion -- 1.7 Do...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Chichester
Wiley
2010
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| Schriftenreihe: | Wiley series in probability and statistics
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| Schlagworte: | |
| Online Zugang: | Verlagsangaben Inhaltsverzeichnis Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | Preface -- 1 Fractional Brownian Motion and Related Processes -- 1.1 Introduction -- 1.2 Self-similar processes -- 1.3 Fractional Brownian motion -- 1.4 Stochastic differential equations driven by fBm -- 1.5 Fractional Ornstein-Uhlenbeck type process -- 1.6 Mixed fractional Brownian motion -- 1.7 Donsker type approximation for fBm with Hurst index H > -- 1.8 Simulation of fractional Brownian motion -- 1.9 Remarks on application of modelling by fBm in mathematical finance -- 1.10 Path wise integration with respect to fBm -- 2 Parametric Estimation for Fractional Diffusion Processes -- 2.1 Introduction -- 2.2 Stochastic differential equations and local asymptotic normality -- 2.3 Parameter estimation for linear SDE -- 2.4 Maximum likelihood estimation -- 2.5 Bayes estimation -- 2.6 Berry-Esseen type bound for MLE -- 2.7-upper and lower functions for MLE -- 2.8 Instrumental variable estimation -- 3 Parametric Estimation for Fractional Ornstein-Uhlenbeck Type Process 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Maximum likelihood estimation -- 3.4 Bayes estimation -- 3.5 Probabilities of large deviations of MLE and BE -- 3.6 Minimum L1-norm estimation -- 4 Sequential Inference for Some Processes Driven by Fractional Brownian -- Motion -- 4.1 Introduction -- 4.2 Sequential maximum likelihood estimation -- 4.3 Sequential testing for simple hypothesis -- 5 Nonparametric Inference for Processes Driven by Fractional Brownian -- Motion -- 5.1 Introduction -- 5.2 Identification for linear stochastic systems -- 5.3 Nonparametric estimation of trend -- 6 Parametric Inference for Some SDE's Driven by Processes Related to FBM 6.1 Introduction -- 6.2 Estimation of the the translation of a process driven by a fBm -- 6.3 Parametric inference for SDE with delay governed by a fBm -- 6.4 Parametric estimation for linear system of SDE driven by fBm's with different Hurst indices -- 6.5 Parametric estimation for SDE driven by mixed fBm -- 6.6 Alternate approach for estimation in models driven by fBm -- 6.7 Maximum likelihood estimation under misspecified model -- 7 Parametric Estimation for Processes Driven by Fractional Brownian Sheet -- 7.1 Introduction -- 7.2 Parametric estimation for linear SDE driven by a fractional Brownian sheet -- 8 Parametric Estimation for Processes Driven by Infinite Dimensional Fractional -- Brownian Motion -- 8.1 Introduction -- 8.2 Parametric estimation for SPDE driven by infinite dimensional fBm -- 8.3 Parametric estimation for stochastic parabolic equations driven by infinite dimensional fBm -- 9 Estimation of Self-Similarity Index -- 9.1 Introduction -- 9.2 Estimation of the Hurst index H when H is a constant and 12 < H < 1 for fBm -- 9.3 Estimation of scaling exponent function H(.) for locally self-similar processes -- 10 Filtering and Prediction for Linear Systems Driven by Fractional Brownian -- Motion -- 10.1 Introduction -- 10.2 Prediction of fractional Brownian motion -- 10.3 Filtering in a simple linear system driven by a fBm -- 10.4 General approach for filtering for linear systems driven by fBm References -- Index |
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| Beschreibung: | Includes bibliographical references (p. [239]-249) and index |
| Beschreibung: | xii, 252 p ill 24 cm |
| ISBN: | 0470665688 0-470-66568-8 9780470665688 978-0-470-66568-8 |