03729nam 22006255 450 991030015730332120200630081407.03-642-54075-910.1007/978-3-642-54075-2(CKB)3710000000088892(SSID)ssj0001187608(PQKBManifestationID)11697479(PQKBTitleCode)TC0001187608(PQKBWorkID)11257166(PQKB)10571662(MiAaPQ)EBC1698230(DE-He213)978-3-642-54075-2(PPN)176751254(EXLCZ)99371000000008889220140212d2014 u| 0engurcnu||||||||txtccrUpper and Lower Bounds for Stochastic Processes[electronic resource] Modern Methods and Classical Problems /by Michel Talagrand1st ed. 2014.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2014.1 online resource (630 pages) illustrationsErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;60Bibliographic Level Mode of Issuance: Monograph3-642-54074-0 Includes bibliographical references and index.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.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 series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out.Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136 ;60ProbabilitiesFunctional analysisProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Probabilities.Functional analysis.Probability Theory and Stochastic Processes.Functional Analysis.519.2510sdnbSK 820rvkTalagrand Michelauthttp://id.loc.gov/vocabulary/relators/aut59814MiAaPQMiAaPQMiAaPQBOOK9910300157303321Upper and lower bounds for stochastic processes821241UNINA