000 03586nam a22005055i 4500
001 978-3-540-27499-5
003 DE-He213
005 20161121230933.0
007 cr nn 008mamaa
008 100301s2005 gw | s |||| 0|eng d
020 _a9783540274995
_9978-3-540-27499-5
024 7 _a10.1007/3-540-27499-5
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aTalagrand, Michel.
_eauthor.
245 1 4 _aThe Generic Chaining
_h[electronic resource] :
_bUpper and Lower Bounds of Stochastic Processes /
_cby Michel Talagrand.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2005.
300 _aVIII, 222 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aOverview and Basic Facts -- Gaussian Processes and Related Structures -- Matching Theorems -- The Bernoulli Conjecture -- Families of distances -- Applications to Banach Space Theory.
520 _aAuthor'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.
650 0 _aMathematics.
650 0 _aApproximation theory.
650 0 _aProbabilities.
650 0 _aStatistics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aApproximations and Expansions.
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540245186
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/3-540-27499-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506145
_d506145