| Edition |
2nd enl. ed. / with an additional chapter by Gyula Pap. |
| Description |
1 online resource (xii, 412 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Series on multivariate analysis ; v. 8
|
|
Series on multivariate analysis ; v. 8.
|
| Note |
Revised edition of: Structural aspects of probability theory. 2004. |
| Bibliography |
Includes bibliographical references (pages 389-395) and index. |
| 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 Ito-Nisio theorem; 3.2 Fourier expansion and construction of Brownian motion. |
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3.3 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. |
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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. |
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III 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. |
| 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 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 wit. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Probabilities.
|
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Probabilities. |
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Topological groups.
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Topological groups. |
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Banach spaces.
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Banach spaces. |
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Probability measures.
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Probability measures. |
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Abelian groups.
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Abelian groups. |
| Genre/Form |
Electronic books.
|
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Electronic books.
|
| Added Author |
Pap, Gyula, 1954-
|
|
Heyer, Herbert.
Structural aspects of probability theory.
|
| Other Form: |
Print version: Heyer, Herbert. Structural aspects in the theory of probability. 2nd ed. New Jersey : World Scientific, 2010 9789814282482 (DLC) 2009021970 (OCoLC)373474750 |
| ISBN |
9789814282499 (electronic book) |
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9814282499 (electronic book) |
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9789814282482 |
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9814282480 |
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