LEADER 03702nam 22006255 450 001 9910300157303321 005 20200630081407.0 010 $a3-642-54075-9 024 7 $a10.1007/978-3-642-54075-2 035 $a(CKB)3710000000088892 035 $a(SSID)ssj0001187608 035 $a(PQKBManifestationID)11697479 035 $a(PQKBTitleCode)TC0001187608 035 $a(PQKBWorkID)11257166 035 $a(PQKB)10571662 035 $a(MiAaPQ)EBC1698230 035 $a(DE-He213)978-3-642-54075-2 035 $a(PPN)176751254 035 $a(EXLCZ)993710000000088892 100 $a20140212d2014 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aUpper and Lower Bounds for Stochastic Processes $eModern Methods and Classical Problems /$fby Michel Talagrand 205 $a1st ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (630 pages) $cillustrations 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v60 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-54074-0 320 $aIncludes bibliographical references and index. 327 $a0. 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. 330 $aThe book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds for Gaussian and Bernoulli processes. Applications are given to stable processes, infinitely divisible processes, matching theorems, the convergence of random Fourier series, of orthogonal series, and to functional analysis. The complete solution of a number of classical problems is given in complete detail, and an ambitious program for future research is laid out. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v60 606 $aProbabilities 606 $aFunctional analysis 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aProbabilities. 615 0$aFunctional analysis. 615 14$aProbability Theory and Stochastic Processes. 615 24$aFunctional Analysis. 676 $a519.2 686 $a510$2sdnb 686 $aSK 820$2rvk 700 $aTalagrand$b Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut$059814 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300157303321 996 $aUpper and lower bounds for stochastic processes$9821241 997 $aUNINA