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| 008 | 170212s2015 gw | s |||| 0|eng d | ||
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_a9783319220994 _9978-3-319-22099-4 |
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_a10.1007/978-3-319-22099-4 _2doi |
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| 040 |
_aSpringer _cSpringer _dRU-ToGU |
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| 050 | 4 | _aQA273.A1-274.9 | |
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_a519.2 _223 |
| 100 | 1 |
_aBercu, Bernard. _eauthor. _9467609 |
|
| 245 | 1 | 0 |
_aConcentration Inequalities for Sums and Martingales _helectronic resource _cby Bernard Bercu, Bernard Delyon, Emmanuel Rio. |
| 250 | _a1st ed. 2015. | ||
| 260 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015. |
||
| 300 |
_aX, 120 p. 9 illus. in color. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 490 | 1 |
_aSpringerBriefs in Mathematics, _x2191-8198 |
|
| 505 | 0 | _aClassical Results -- Concentration Inequalities for Sums -- Concentration Inequalities for Martingales -- Applications in Probability and Statistics. | |
| 520 | _aThe purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics. | ||
| 650 | 0 |
_amathematics. _9566183 |
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| 650 | 0 |
_aFunctions of complex variables. _9304502 |
|
| 650 | 0 |
_aHistory. _9303998 |
|
| 650 | 0 |
_aProbabilities. _9295556 |
|
| 650 | 1 | 4 |
_aMathematics. _9566184 |
| 650 | 2 | 4 |
_aProbability Theory and Stochastic Processes. _9303734 |
| 650 | 2 | 4 |
_aHistory of Mathematical Sciences. _9296777 |
| 650 | 2 | 4 |
_aSeveral Complex Variables and Analytic Spaces. _9304717 |
| 700 | 1 |
_aDelyon, Bernard. _eauthor. _9467610 |
|
| 700 | 1 |
_aRio, Emmanuel. _eauthor. _9467611 |
|
| 710 | 2 |
_aSpringerLink (Online service) _9143950 |
|
| 773 | 0 | _tSpringer eBooks | |
| 830 | 0 |
_aSpringerBriefs in Mathematics, _9445669 |
|
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-319-22099-4 |
| 912 | _aZDB-2-SMA | ||
| 999 | _c415267 | ||