LEADER 04503nam 22006735 450 001 9910299986003321 005 20200630080112.0 010 $a3-662-44388-0 024 7 $a10.1007/978-3-662-44388-0 035 $a(CKB)3710000000261991 035 $a(EBL)1967460 035 $a(OCoLC)896834269 035 $a(SSID)ssj0001372688 035 $a(PQKBManifestationID)11881981 035 $a(PQKBTitleCode)TC0001372688 035 $a(PQKBWorkID)11304526 035 $a(PQKB)10857010 035 $a(MiAaPQ)EBC1967460 035 $a(DE-He213)978-3-662-44388-0 035 $a(PPN)182097196 035 $a(EXLCZ)993710000000261991 100 $a20141013d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLimit Theorems for Multi-Indexed Sums of Random Variables$b[electronic resource] /$fby Oleg Klesov 205 $a1st ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (495 p.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v71 300 $aDescription based upon print version of record. 311 $a3-662-44387-2 320 $aIncludes bibliographical references and index. 327 $a1.Notation and auxiliary results -- 2.Maximal inequalities for multiple sums -- 3.Weak convergence of multiple sums -- 4.Weak law of large numbers for multiple sums -- 5.Almost sure convergence for multiple series -- 6.Boundedness of multiple series -- 7.Rate of convergence of multiple sums -- 8.Strong law of large numbers for independent non-identically distributed random variables -- 9.Strong law of large numbers for independent identically distributed random variables -- 10.Law of the iterated logarithm -- 11.Renewal theorem for random walks with multidimensional time -- 12.Existence of moments of the supremum of multiple sums and the strong law of large numbers -- 13.Complete convergence. 330 $aPresenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v71 606 $aProbabilities 606 $aStatistics  606 $aPhysics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aProbabilities. 615 0$aStatistics . 615 0$aPhysics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aStatistical Theory and Methods. 615 24$aMathematical Methods in Physics. 676 $a518.1 700 $aKlesov$b Oleg$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721198 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299986003321 996 $aLimit theorems for multi-indexed sums of random variables$91409960 997 $aUNINA