Long-range dependence and self-similarity
著者
書誌事項
Long-range dependence and self-similarity
（Cambridge series on statistical and probabilistic mathematics）
Cambridge University Press, 2017
- : hardback
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注記
Includes bibliographical references (p. 613-659) and index
内容説明・目次
内容説明
This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.
目次
- List of abbreviations
- Notation
- Preface
- 1. A brief overview of times series and stochastic processes
- 2. Basics of long-range dependence and self-similarity
- 3. Physical models for long-range dependence and self-similarity
- 4. Hermite processes
- 5. Non-central and central limit theorems
- 6. Fractional calculus and integration of deterministic functions with respect to FBM
- 7. Stochastic integration with respect to fractional Brownian motion
- 8. Series representations of fractional Brownian motion
- 9. Multidimensional models
- 10. Maximum likelihood estimation methods
- Appendix A. Auxiliary notions and results
- Appendix B. Integrals with respect to random measures
- Appendix C. Basics of Malliavin calculus
- Appendix D. Other notes and topics
- Bibliography
- Index.
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