A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.
A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.
Vladas Pipiras is Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. His research focuses on stochastic processes exhibiting long-range dependence, self-similarity, and other scaling phenomena, as well as on stable, extreme-value and other distributions possessing heavy tails. His other current interests include high-dimensional time series, sampling issues for 'big data', and stochastic dynamical systems, with applications in econometrics, neuroscience, engineering, computer science, and other areas. He has written over fifty research papers and is coauthor of A Basic Course in Measure and Probability: Theory for Applications (with Ross Leadbetter and Stamatis Cambanis, Cambridge, 2014)
Inhaltsangabe
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.
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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