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050  4 QA273.43 -- .H53 2009eb 
082 0  519.2 
100 1  Heyer, Herbert 
245 10 Structural Aspects in the Theory of Probability 
250    2nd ed 
264  1 Singapore :|bWorld Scientific Publishing Co Pte Ltd,|c2009
264  4 |c©2009 
300    1 online resource (425 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  World Scientific Series In Nanoscience And Nanotechnology 
       ;|vv.8 
505 0  Intro -- 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 motion -- 3.3 Symmetric Levy measures and 
       generalized Poisson measures -- 3.4 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 -- 6.2 The transience criterion -- 
       6.3 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 
505 8  III Gaussian processes in a Sturm-Liouville hypergroup -- 
       Comments 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 
520    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 with the 
       relevant facts of harmonic analysis make it possible to 
       study certain properties of stochastic processes in 
       dependence of the algebraic-topological structure of their
       state spaces. In extension of the first edition, the new 
       edition contains chapters on the probability theory of 
       generalized convolution structures such as polynomial and 
       Sturm-Liouville hypergroups, and on the central limit 
       problem for groups such as tori, p-adic groups and 
       solenoids. Sample Chapter(s). Chapter 1: Probability 
       Measures on Metric Spaces (318 KB). Contents: Probability 
       Measures on Metric Spaces; The Fourier Transform in a 
       Banach Space; The Structure of Infinitely Divisible 
       Probability Measures; Harmonic Analysis of Convolution 
       Semigroups; Negative Definite Functions and Convolution 
       Semigroups; Probabilistic Properties of Convolution 
       Semigroups; Hypergroups in Probability Theory; Limit 
       Theorems on Locally Compact Abelian Groups. Readership: 
       Graduate students, lecturers and researchers in 
       probability and statistics 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Probabilities.;Topological groups.;Banach 
       spaces.;Probability measures.;Abelian groups 
655  4 Electronic books 
776 08 |iPrint version:|aHeyer, Herbert|tStructural Aspects in 
       the Theory of Probability|dSingapore : World Scientific 
       Publishing Co Pte Ltd,c2009|z9789814282482 
830  0 World Scientific Series In Nanoscience And Nanotechnology 
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
       detail.action?docID=1679582|zClick to View