05038nam 2200745Ia 450 991078072270332120230721024354.01-282-76140-49786612761409981-4282-49-9(CKB)2490000000001657(EBL)1679582(OCoLC)880826795(SSID)ssj0000442872(PQKBManifestationID)11293181(PQKBTitleCode)TC0000442872(PQKBWorkID)10447568(PQKB)10921131(MiAaPQ)EBC1679582(WSP)00000587 (Au-PeEL)EBL1679582(CaPaEBR)ebr10422517(CaONFJC)MIL276140(EXLCZ)99249000000000165720090604d2009 uy 0engur|n|---|||||txtccrStructural aspects in the theory of probability[electronic resource] /by Herbert Heyer2nd ed. /with an additional chapeter by Gyula Pap.New Jersey World Scientific20091 online resource (425 p.)Series on multivariate analysis ;v. 8Rev. ed. of: Structural aspects of probability theory. 2004.981-4282-48-0 Includes bibliographical references and index.Contents; 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 motion3.3 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 semigroups6.2 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 processesIII 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 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 wiSeries on multivariate analysis ;v. 8.ProbabilitiesTopological groupsBanach spacesProbability measuresAbelian groupsProbabilities.Topological groups.Banach spaces.Probability measures.Abelian groups.519.2Heyer Herbert47694Pap Gyula1519817Heyer Herbert47694MiAaPQMiAaPQMiAaPQBOOK9910780722703321Structural aspects in the theory of probability3758110UNINA