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Upper and Lower Bounds for Stochastic Processes: Modern Methods and Classical Problems de Michel Talagrand

Upper and Lower Bounds for Stochastic Processes: Modern Methods and Classical Problems: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, cartea 60

Autor Michel Talagrand
en Limba Engleză Hardback – 20 feb 2014
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.
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Specificații

ISBN-13: 9783642540745
ISBN-10: 3642540740
Pagini: 644
Dimensiuni: 155 x 235 x 40 mm
Greutate: 1.07 kg
Ediția:2014
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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 isReallyAbout.- 18. Appendix: Continuity.- References. Index.

Recenzii

“Although he writes a book about inequalities of stochastic processes, Talagrand focuses on modern abstract methods, completely abdicating the ‘classical approach’. … Talagrand’s goal in this book is, without any doubt, very ambitious. … it contains marvelous ideas that should very likely be in the toolbox of anyone dealing with stochastic processes.” (Antonio Auffinger, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)
“Each chapter begins with an explanation of the overall philosophy and gives a brief survey of the things to come. This makes a rewarding read for everyone with a sound probability background, and for the specialist it is even entertaining and most inspiring. … There are many areas where Talagrand has a very personal view of things which, I am sure, will be food for thought for future generations of probabilists.” (René L. Schilling, The Mathematical Gazette, Vol. 100 (547), 2016)
“The topic of this book is the study of the supremum of certain stochastic processes, more precisely, it describes how to find upper and lower bounds for this suprema. … The book can be interesting for all potential readers who study the modern stochastic methods, for undergraduate and postgraduate students, for specialists in the theory of stochastic processes and for practitioners who treat the trajectories of stochastic models.” (Yuliya S. Mishura, zbMATH, Vol. 1293, 2014)

Caracteristici

Develops modern methods and in particular the "generic chaining" to bound stochastic processes
Gives applications to stable processes, infinitely divisible processes, matching theorems etc.
Gives the complete solution of a number of classical problems
Includes supplementary material: sn.pub/extras

Notă biografică

Michel Talagrand has made profound contributions to mathematics, notably in probability theory and related topics. The author of several books and well over 200 research papers, he is the recipient of several awards, including the Loève Prize, the Fermat Prize and the Shaw Prize. He has been a plenary speaker at the International Congress of Mathematicians and is a member of the French Academy of Sciences.