Inequalities in analysis and probability:
The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bound...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2013
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| Schlagworte: | |
| Zusammenfassung: | The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail Preface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Cauchy and Holder inequalities; 1.3 Inequalities for transformed series and functions; 1.4 Applications in probability; 1.5 Hardy's inequality; 1.6 Inequalities for discrete martingales; 1.7 Martingales indexed by continuous parameters; 1.8 Large deviations and exponential inequalities; 1.9 Functional inequalities; 1.10 Content of the book; 2. Inequalities for Means and Integrals; 2.1 Introduction; 2.2 Inequalities for means in real vector spaces; 2.3 Holder and Hilbert inequalities; 2.4 Generalizations of Hardy's inequality. - 2.5 Carleman's inequality and generalizations2.6 Minkowski's inequality and generalizations; 2.7 Inequalities for the Laplace transform; 2.8 Inequalities for multivariate functions; 3. Analytic Inequalities; 3.1 Introduction; 3.2 Bounds for series; 3.3 Cauchy's inequalities and convex mappings; 3.4 Inequalities for the mode and the median; 3.5 Mean residual time; 3.6 Functional equations; 3.7 Carlson's inequality; 3.8 Functional means; 3.9 Young's inequalities; 3.10 Entropy and information; 4. Inequalities for Martingales; 4.1 Introduction. - 4.2 Inequalities for sums of independent random variables4.3 Inequalities for discrete martingales; 4.4 Inequalities for martingales indexed by R+; 4.5 Poisson processes; 4.6 Brownian motion; 4.7 Diffusion processes; 4.8 Level crossing probabilities; 4.9 Martingales in the plane; 5. Functional Inequalities; 5.1 Introduction; 5.2 Exponential inequalities for functional empirical processes; 5.3 Exponential inequalities for functional martingales; 5.4 Weak convergence of functional processes; 5.5 Differentiable functionals of empirical processes; 5.6 Regression functions and biased length |
| Beschreibung: | IX, 221 S. graph. Darst. |
| ISBN: | 9789814412575 |
Internformat
MARC
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| 520 | 1 | |a The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail | |
| 520 | 8 | |a Preface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Cauchy and Holder inequalities; 1.3 Inequalities for transformed series and functions; 1.4 Applications in probability; 1.5 Hardy's inequality; 1.6 Inequalities for discrete martingales; 1.7 Martingales indexed by continuous parameters; 1.8 Large deviations and exponential inequalities; 1.9 Functional inequalities; 1.10 Content of the book; 2. Inequalities for Means and Integrals; 2.1 Introduction; 2.2 Inequalities for means in real vector spaces; 2.3 Holder and Hilbert inequalities; 2.4 Generalizations of Hardy's inequality. - 2.5 Carleman's inequality and generalizations2.6 Minkowski's inequality and generalizations; 2.7 Inequalities for the Laplace transform; 2.8 Inequalities for multivariate functions; 3. Analytic Inequalities; 3.1 Introduction; 3.2 Bounds for series; 3.3 Cauchy's inequalities and convex mappings; 3.4 Inequalities for the mode and the median; 3.5 Mean residual time; 3.6 Functional equations; 3.7 Carlson's inequality; 3.8 Functional means; 3.9 Young's inequalities; 3.10 Entropy and information; 4. Inequalities for Martingales; 4.1 Introduction. - 4.2 Inequalities for sums of independent random variables4.3 Inequalities for discrete martingales; 4.4 Inequalities for martingales indexed by R+; 4.5 Poisson processes; 4.6 Brownian motion; 4.7 Diffusion processes; 4.8 Level crossing probabilities; 4.9 Martingales in the plane; 5. Functional Inequalities; 5.1 Introduction; 5.2 Exponential inequalities for functional empirical processes; 5.3 Exponential inequalities for functional martingales; 5.4 Weak convergence of functional processes; 5.5 Differentiable functionals of empirical processes; 5.6 Regression functions and biased length | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Pons, Odile 1953- |
| author_GND | (DE-588)1158864035 |
| author_facet | Pons, Odile 1953- |
| author_role | aut |
| author_sort | Pons, Odile 1953- |
| author_variant | o p op |
| building | Verbundindex |
| bvnumber | BV040907778 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)844040209 (DE-599)BSZ379331586 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040907778 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:01Z |
| institution | BVB |
| isbn | 9789814412575 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025887169 |
| oclc_num | 844040209 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM DE-824 DE-83 |
| owner_facet | DE-384 DE-19 DE-BY-UBM DE-824 DE-83 |
| physical | IX, 221 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Pons, Odile 1953- Verfasser (DE-588)1158864035 aut Inequalities in analysis and probability Odile Pons Singapore [u.a.] World Scientific 2013 IX, 221 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of the new results are presented in great detail Preface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Cauchy and Holder inequalities; 1.3 Inequalities for transformed series and functions; 1.4 Applications in probability; 1.5 Hardy's inequality; 1.6 Inequalities for discrete martingales; 1.7 Martingales indexed by continuous parameters; 1.8 Large deviations and exponential inequalities; 1.9 Functional inequalities; 1.10 Content of the book; 2. Inequalities for Means and Integrals; 2.1 Introduction; 2.2 Inequalities for means in real vector spaces; 2.3 Holder and Hilbert inequalities; 2.4 Generalizations of Hardy's inequality. - 2.5 Carleman's inequality and generalizations2.6 Minkowski's inequality and generalizations; 2.7 Inequalities for the Laplace transform; 2.8 Inequalities for multivariate functions; 3. Analytic Inequalities; 3.1 Introduction; 3.2 Bounds for series; 3.3 Cauchy's inequalities and convex mappings; 3.4 Inequalities for the mode and the median; 3.5 Mean residual time; 3.6 Functional equations; 3.7 Carlson's inequality; 3.8 Functional means; 3.9 Young's inequalities; 3.10 Entropy and information; 4. Inequalities for Martingales; 4.1 Introduction. - 4.2 Inequalities for sums of independent random variables4.3 Inequalities for discrete martingales; 4.4 Inequalities for martingales indexed by R+; 4.5 Poisson processes; 4.6 Brownian motion; 4.7 Diffusion processes; 4.8 Level crossing probabilities; 4.9 Martingales in the plane; 5. Functional Inequalities; 5.1 Introduction; 5.2 Exponential inequalities for functional empirical processes; 5.3 Exponential inequalities for functional martingales; 5.4 Weak convergence of functional processes; 5.5 Differentiable functionals of empirical processes; 5.6 Regression functions and biased length Analysis (DE-588)4001865-9 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Analysis (DE-588)4001865-9 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Integrationstheorie (DE-588)4138369-2 s Ungleichung (DE-588)4139098-2 s DE-604 |
| spellingShingle | Pons, Odile 1953- Inequalities in analysis and probability Analysis (DE-588)4001865-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Integrationstheorie (DE-588)4138369-2 gnd Ungleichung (DE-588)4139098-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4079013-7 (DE-588)4138369-2 (DE-588)4139098-2 |
| title | Inequalities in analysis and probability |
| title_auth | Inequalities in analysis and probability |
| title_exact_search | Inequalities in analysis and probability |
| title_full | Inequalities in analysis and probability Odile Pons |
| title_fullStr | Inequalities in analysis and probability Odile Pons |
| title_full_unstemmed | Inequalities in analysis and probability Odile Pons |
| title_short | Inequalities in analysis and probability |
| title_sort | inequalities in analysis and probability |
| topic | Analysis (DE-588)4001865-9 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Integrationstheorie (DE-588)4138369-2 gnd Ungleichung (DE-588)4139098-2 gnd |
| topic_facet | Analysis Wahrscheinlichkeitstheorie Integrationstheorie Ungleichung |
| work_keys_str_mv | AT ponsodile inequalitiesinanalysisandprobability |