LEADER 05038nam 2200745Ia 450 001 9910780722703321 005 20230721024354.0 010 $a1-282-76140-4 010 $a9786612761409 010 $a981-4282-49-9 035 $a(CKB)2490000000001657 035 $a(EBL)1679582 035 $a(OCoLC)880826795 035 $a(SSID)ssj0000442872 035 $a(PQKBManifestationID)11293181 035 $a(PQKBTitleCode)TC0000442872 035 $a(PQKBWorkID)10447568 035 $a(PQKB)10921131 035 $a(MiAaPQ)EBC1679582 035 $a(WSP)00000587 035 $a(Au-PeEL)EBL1679582 035 $a(CaPaEBR)ebr10422517 035 $a(CaONFJC)MIL276140 035 $a(EXLCZ)992490000000001657 100 $a20090604d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStructural aspects in the theory of probability$b[electronic resource] /$fby Herbert Heyer 205 $a2nd ed. /$bwith an additional chapeter by Gyula Pap. 210 $aNew Jersey $cWorld Scientific$d2009 215 $a1 online resource (425 p.) 225 1 $aSeries on multivariate analysis ;$vv. 8 300 $aRev. ed. of: Structural aspects of probability theory. 2004. 311 $a981-4282-48-0 320 $aIncludes bibliographical references and index. 327 $aContents; Preface to the second enlarged edition; Preface; 1. Probability Measures on Metric Spaces; 1.1 Tight measures; 1.2 The topology of weak convergence; 1.3 The Prokhorov theorem; 1.4 Convolution of measures; 2. The Fourier Transform in a Banach Space; 2.1 Fourier transforms of probability measures; 2.2 Shift compact sets of probability measures; 2.3 Infinitely divisible and embeddable measures; 2.4 Gauss and Poisson measures; 3. The Structure of In nitely Divisible Probability Measures; 3.1 The Ito-Nisio theorem; 3.2 Fourier expansion and construction of Brownian motion 327 $a3.3 Symmetric Levy measures and generalized Poisson measures3.4 The Levy-Khinchin decomposition; 4. Harmonic Analysis of Convolution Semigroups; 4.1 Convolution of Radon measures; 4.2 Duality of locally compact Abelian groups; 4.3 Positive definite functions; 4.4 Positive definite measures; 5. Negative Definite Functions and Convolution Semigroups; 5.1 Negative definite functions; 5.2 Convolution semigroups and resolvents; 5.3 Levy functions; 5.4 The L evy-Khinchin representation; 6. Probabilistic Properties of Convolution Semigroups; 6.1 Transient convolution semigroups 327 $a6.2 The transience criterion6.3 Recurrent random walks; 6.4 Classification of transient random walks; 7. Hypergroups in Probability Theory; 7.1 Commutative hypergroups; I Introduction to hypergroups; II Some analysis on hypergroups; 7.2 Decomposition of convolution semigroups of measures; I Constructions of hypergroups; II Convolution semigroup of measures; 7.3 Random walks in hypergroups; I Transient random walks; II Limit theorems for random walks; 7.4 Increment processes and convolution semigroups; I Modification of increment processes; II Martingale characterizations of L evy processes 327 $aIII Gaussian processes in a Sturm-Liouville hypergroupComments on the selection of references; 8. Limit Theorems on Locally Compact Abelian Groups; 8.1 Limit problems and parametrization of weakly infinitely divisible measures; 8.2 Gaiser's limit theorem; 8.3 Limit theorems for symmetric arrays and Bernoulli arrays; 8.4 Limit theorems for special locally compact Abelian groups; Appendices; A Topological groups; B Topological vector spaces; C Commutative Banach algebras; Selected References; Symbols; Index 330 $a The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation - the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups - is given an in-depth discussion. This powerful analytic tool along wi 410 0$aSeries on multivariate analysis ;$vv. 8. 606 $aProbabilities 606 $aTopological groups 606 $aBanach spaces 606 $aProbability measures 606 $aAbelian groups 615 0$aProbabilities. 615 0$aTopological groups. 615 0$aBanach spaces. 615 0$aProbability measures. 615 0$aAbelian groups. 676 $a519.2 700 $aHeyer$b Herbert$047694 701 $aPap$b Gyula$01519817 701 $aHeyer$b Herbert$047694 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780722703321 996 $aStructural aspects in the theory of probability$93758110 997 $aUNINA