Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Upper and Lower Bounds for Stochastic Processes

Modern Methods and Classical Problems

Authors: Talagrand, Michel

  • 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
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About this book

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.

Reviews

“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)

Table of contents (16 chapters)

  • Philosophy and Overview of the Book

    Talagrand, Michel

    Pages 1-12

  • Gaussian Processes and the Generic Chaining

    Talagrand, Michel

    Pages 13-73

  • Random Fourier Series and Trigonometric Sums, I

    Talagrand, Michel

    Pages 75-89

  • Matching Theorems, I

    Talagrand, Michel

    Pages 91-127

  • Bernoulli Processes

    Talagrand, Michel

    Pages 129-171

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-54075-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-642-54074-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-662-52546-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Upper and Lower Bounds for Stochastic Processes
Book Subtitle
Modern Methods and Classical Problems
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
60
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-54075-2
DOI
10.1007/978-3-642-54075-2
Hardcover ISBN
978-3-642-54074-5
Softcover ISBN
978-3-662-52546-3
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XV, 626
Topics