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010   $a3-319-22099-3
024 7 $a10.1007/978-3-319-22099-4
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100   $a20150929d2015      u|             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aConcentration inequalities for sums and martingales$b[electronic resource] /$fby Bernard Bercu, Bernard Delyon, Emmanuel Rio
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (131 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a3-319-22098-5 
320   $aIncludes bibliographical references at the end of each chapters.
327   $aClassical Results -- Concentration Inequalities for Sums -- Concentration Inequalities for Martingales -- Applications in Probability and Statistics.
330   $aThe purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aProbabilities
606   $aMathematics
606   $aHistory
606   $aFunctions of complex variables
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
615  0$aProbabilities.
615  0$aMathematics.
615  0$aHistory.
615  0$aFunctions of complex variables.
615 14$aProbability Theory and Stochastic Processes.
615 24$aHistory of Mathematical Sciences.
615 24$aSeveral Complex Variables and Analytic Spaces.
676   $a510
700   $aBercu$b Bernard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755639
702   $aDelyon$b Bernard$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aRio$b Emmanuel$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300243303321
996   $aConcentration Inequalities for Sums and Martingales$92536510
997   $aUNINA