Author 
Heyer, Herbert.

Series 
Series on multivariate analysis ; v. 8 

Series on multivariate analysis ;
v. 8.

Subject 
Probabilities.


Topological groups.


Banach spaces.


Probability measures.


Abelian groups.

Alt Name 
Pap, Gyula.


Heyer, Herbert.
Structural aspects of probability theory.

Description 
1 online resource (xii, 412 pages) 
Edition 
2nd enl. ed. / with an additional chapter by Gyula Pap. 
Bibliography Note 
Includes bibliographical references (pages 389395) and index. 
Note 
Print version record. 
Contents 
Preface to the second enlarged edition; Preface; Contents; 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 ItoNisio theorem; 3.2 Fourier expansion and construction of Brownian motion. 

3.3 Symmetric Levy measures and generalized Poisson measures3.4 The LevyKhinchin 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 evyKhinchin representation; 6. Probabilistic Properties of Convolution Semigroups; 6.1 Transient convolution semigroups. 

6.2 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. 

III Gaussian processes in a SturmLiouville 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. 
Summary 
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 algebraictopological 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 indepth discussion. This powerful analytic tool along wit. 
ISBN 
9789814282499 (electronic bk.) 

9814282499 (electronic bk.) 

9789814282482 

9814282480 
OCLC # 
696139086 
Additional Format 
Print version: Heyer, Herbert. Structural aspects in the theory of probability. 2nd ed. New Jersey : World Scientific, 2010 9789814282482 (DLC) 2009021970 (OCoLC)373474750 
