Structural aspects in the theory of probability /:
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 continuo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey :
World Scientific,
©2010.
|
| Ausgabe: | 2nd enl. ed. / |
| Schriftenreihe: | Series on multivariate analysis ;
v. 8. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xii, 412 pages) |
| Bibliographie: | Includes bibliographical references (pages 389-395) and index. |
| ISBN: | 9789814282499 9814282499 |
Internformat
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| 250 | |a 2nd enl. ed. / |b with an additional chapter by Gyula Pap. | ||
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| 300 | |a 1 online resource (xii, 412 pages) | ||
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| 490 | 1 | |a Series on multivariate analysis ; |v v. 8 | |
| 504 | |a Includes bibliographical references (pages 389-395) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
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| 650 | 0 | |a Topological groups. |0 http://id.loc.gov/authorities/subjects/sh85136082 | |
| 650 | 0 | |a Banach spaces. |0 http://id.loc.gov/authorities/subjects/sh85011441 | |
| 650 | 0 | |a Probability measures. |0 http://id.loc.gov/authorities/subjects/sh92001869 | |
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| 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. 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. 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 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. |
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| dewey-full | 519.2 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd enl. ed. / |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn696139086 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-18T14:15:26Z |
| institution | BVB |
| isbn | 9789814282499 9814282499 |
| language | English |
| oclc_num | 696139086 |
| open_access_boolean | |
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| publishDateSort | 2009 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on multivariate analysis ; |
| series2 | Series on multivariate analysis ; |
| spelling | Heyer, Herbert. http://id.loc.gov/authorities/names/n79041598 Structural aspects in the theory of probability / Herbert Heyer. 2nd enl. ed. / with an additional chapter by Gyula Pap. New Jersey : World Scientific, ©2010. 1 online resource (xii, 412 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Series on multivariate analysis ; v. 8 Includes bibliographical references (pages 389-395) and index. Print version record. 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. 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. 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 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 wit. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Topological groups. http://id.loc.gov/authorities/subjects/sh85136082 Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Probability measures. http://id.loc.gov/authorities/subjects/sh92001869 Abelian groups. http://id.loc.gov/authorities/subjects/sh85000128 Probability https://id.nlm.nih.gov/mesh/D011336 Probabilités. Groupes topologiques. Espaces de Banach. Mesures de probabilités. Groupes abéliens. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Abelian groups fast Banach spaces fast Probabilities fast Probability measures fast Topological groups fast Pap, Gyula. Heyer, Herbert. Structural aspects of probability theory. has work: Structural aspects in the theory of probability (Text) https://id.oclc.org/worldcat/entity/E39PCH6k3wfJpFtbc68WxPJKJP https://id.oclc.org/worldcat/ontology/hasWork Print version: Heyer, Herbert. Structural aspects in the theory of probability. 2nd ed. New Jersey : World Scientific, 2010 9789814282482 (DLC) 2009021970 (OCoLC)373474750 Series on multivariate analysis ; v. 8. http://id.loc.gov/authorities/names/n95093809 |
| spellingShingle | Heyer, Herbert Structural aspects in the theory of probability / Series on multivariate analysis ; 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. 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. 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 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. Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Topological groups. http://id.loc.gov/authorities/subjects/sh85136082 Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Probability measures. http://id.loc.gov/authorities/subjects/sh92001869 Abelian groups. http://id.loc.gov/authorities/subjects/sh85000128 Probability https://id.nlm.nih.gov/mesh/D011336 Probabilités. Groupes topologiques. Espaces de Banach. Mesures de probabilités. Groupes abéliens. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Abelian groups fast Banach spaces fast Probabilities fast Probability measures fast Topological groups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85107090 http://id.loc.gov/authorities/subjects/sh85136082 http://id.loc.gov/authorities/subjects/sh85011441 http://id.loc.gov/authorities/subjects/sh92001869 http://id.loc.gov/authorities/subjects/sh85000128 https://id.nlm.nih.gov/mesh/D011336 |
| title | Structural aspects in the theory of probability / |
| title_alt | Structural aspects of probability theory. |
| title_auth | Structural aspects in the theory of probability / |
| title_exact_search | Structural aspects in the theory of probability / |
| title_full | Structural aspects in the theory of probability / Herbert Heyer. |
| title_fullStr | Structural aspects in the theory of probability / Herbert Heyer. |
| title_full_unstemmed | Structural aspects in the theory of probability / Herbert Heyer. |
| title_short | Structural aspects in the theory of probability / |
| title_sort | structural aspects in the theory of probability |
| topic | Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Topological groups. http://id.loc.gov/authorities/subjects/sh85136082 Banach spaces. http://id.loc.gov/authorities/subjects/sh85011441 Probability measures. http://id.loc.gov/authorities/subjects/sh92001869 Abelian groups. http://id.loc.gov/authorities/subjects/sh85000128 Probability https://id.nlm.nih.gov/mesh/D011336 Probabilités. Groupes topologiques. Espaces de Banach. Mesures de probabilités. Groupes abéliens. probability. aat MATHEMATICS Probability & Statistics General. bisacsh Abelian groups fast Banach spaces fast Probabilities fast Probability measures fast Topological groups fast |
| topic_facet | Probabilities. Topological groups. Banach spaces. Probability measures. Abelian groups. Probability Probabilités. Groupes topologiques. Espaces de Banach. Mesures de probabilités. Groupes abéliens. probability. MATHEMATICS Probability & Statistics General. Abelian groups Banach spaces Probabilities Probability measures Topological groups |
| work_keys_str_mv | AT heyerherbert structuralaspectsinthetheoryofprobability AT papgyula structuralaspectsinthetheoryofprobability |