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Record Nr. |
UNINA9910300157303321 |
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Autore |
Talagrand Michel |
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Titolo |
Upper and Lower Bounds for Stochastic Processes : Modern Methods and Classical Problems / / by Michel Talagrand |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (630 pages) : illustrations |
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Collana |
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Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, , 0071-1136 ; ; 60 |
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Classificazione |
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Disciplina |
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Soggetti |
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Probabilities |
Functional analysis |
Probability Theory and Stochastic Processes |
Functional Analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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0. Introduction -- 1. Philosophy and Overview of the Book -- 2. Gaussian Processes and the Generic Chaining -- 3. Random Fourier Series and Trigonometric Sums, I. - 4. Matching Theorems I -- 5. Bernouilli Processes -- 6. Trees and the Art of Lower Bounds -- 7. Random Fourier Series and Trigonometric Sums, II -- 8. Processes Related to Gaussian Processes -- 9. Theory and Practice of Empirical Processes -- 10. Partition Scheme for Families of Distances -- 11. Infinitely Divisible Processes -- 12. The Fundamental Conjectures -- 13. Convergence of Orthogonal Series; Majorizing Measures -- 14. Matching Theorems, II: Shor's Matching Theorem. 15. The Ultimate Matching Theorem in Dimension ≥ 3 -- 16. Applications to Banach Space Theory -- 17. Appendix: What this Book is Really About -- 18. Appendix: Continuity -- References. Index. |
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Sommario/riassunto |
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The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier |
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