The Generic Chaining

The Generic Chaining
Author :
Publisher : Springer Science & Business Media
Total Pages : 227
Release :
ISBN-10 : 9783540274995
ISBN-13 : 3540274995
Rating : 4/5 (995 Downloads)

Book Synopsis The Generic Chaining by : Michel Talagrand

Download or read book The Generic Chaining written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "Upper and Lower Bounds for Stochastic Processes" (Ergebnisse Vol. 60, ISBN 978-3-642-54074-5). That 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.


The Generic Chaining Related Books

The Generic Chaining
Language: en
Pages: 227
Authors: Michel Talagrand
Categories: Mathematics
Type: BOOK - Published: 2005-12-08 - Publisher: Springer Science & Business Media

GET EBOOK

Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "Upper and Lower Bounds f
Upper and Lower Bounds for Stochastic Processes
Language: en
Pages: 630
Authors: Michel Talagrand
Categories: Mathematics
Type: BOOK - Published: 2014-02-12 - Publisher: Springer Science & Business Media

GET EBOOK

The book develops modern methods and in particular the "generic chaining" to bound stochastic processes. This methods allows in particular to get optimal bounds
The Generic Chaining
Language: en
Pages: 0
Authors: Michel Talagrand
Categories: Mathematics
Type: BOOK - Published: 2005-03-17 - Publisher: Springer

GET EBOOK

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fer
High-Dimensional Probability
Language: en
Pages: 299
Authors: Roman Vershynin
Categories: Business & Economics
Type: BOOK - Published: 2018-09-27 - Publisher: Cambridge University Press

GET EBOOK

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Upper and Lower Bounds for Stochastic Processes
Language: en
Pages: 727
Authors: Michel Talagrand
Categories: Mathematics
Type: BOOK - Published: 2022-01-01 - Publisher: Springer Nature

GET EBOOK

This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader