000 | 03586nam a22005055i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/3-540-27499-5 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
072 | 7 |
_aPBT _2bicssc |
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072 | 7 |
_aPBWL _2bicssc |
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072 | 7 |
_aMAT029000 _2bisacsh |
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082 | 0 | 4 |
_a519.2 _223 |
100 | 1 |
_aTalagrand, Michel. _eauthor. |
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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. |
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300 |
_aVIII, 222 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
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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 |