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Springer Monographs in Mathematics

The Generic Chaining

Upper and Lower Bounds of Stochastic Processes

Authors: Talagrand, Michel

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About this book

Author's Note: 
The material of this book has been reworked and expanded with a lot more details and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978-3-642-54074-5). This book is much easier to read and covers everything that is in "The Generic Chaining" book in a more detailed and comprehensible way.   
************What is the maximum level a certain river is likely to reach over the next 25 years? (Having experienced three times a few feet of water in my house, I feel a keen personal interest in this question. ) There are many questions of the same nature: what is the likely magnitude of the strongest earthquake to occur during the life of a planned building, or the speed of the strongest wind a suspension bridge will have to stand? All these situations can be modeled in the same manner. The value X of the quantity of interest (be it water t level or speed of wind) at time t is a random variable. What can be said about the maximum value of X over a certain range of t? t A collection of random variables (X ), where t belongs to a certain index t set T, is called a stochastic process, and the topic of this book is the study of the supremum of certain stochastic processes, and more precisely to ?nd upper and lower bounds for the quantity EsupX . (0. 1) t t?T Since T might be uncountable, some care has to be taken to de?ne this quantity. For any reasonable de?nition of Esup X we have t t?T EsupX =sup{EsupX ; F?T,F ?nite} , (0. 2) t t t?T t?F an equality that we will take as the de?nition of the quantity Esup X . t t?T Thus, the crucial case for the estimation of the quantity (0.



Reviews

From the reviews:

"This textbook gives a systematic approach to the problem of deriving good bounds for stochastic processes using the ‘generic chaining’ method … . The presentation in this book … takes the reader from a simple and intuitive explanation of the basic idea underlying the chaining technique to the edge of today’s knowledge. … The entertaining and sometimes humorous style makes this book a pleasure to read." (Dierk Peithmann, Zentralblatt MATH, Vol. 1075, 2006)

"The results discussed in the book involve a tremendous amount of creativity … . I believe that the monograph is of interest to anyone who works even remotely with indexed families of maps… . is of interest to almost everyone who works in probability, analysis, or ergodic theory even if she/he has not done any research involving the topics covered by the volume under review. … I want to emphasize the fact that the book is of interest to a larger audience … ." (Radu Zaharopol, SIAM Review, Vol. 49 (2), 2007)


Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-540-27499-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-540-24518-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-642-06386-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Generic Chaining
Book Subtitle
Upper and Lower Bounds of Stochastic Processes
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-27499-5
DOI
10.1007/3-540-27499-5
Hardcover ISBN
978-3-540-24518-6
Softcover ISBN
978-3-642-06386-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
VIII, 222
Topics