Inequalities in Analysis and Probability:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Singapore
World Scientific
2012
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Schlagworte: | |
Online-Zugang: | FAW01 FAW02 Volltext |
Beschreibung: | 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 Includes bibliographical references and index 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 generalizations. 2.6. 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 variables. 4.3. Inequalities for discrete martingales. 4.4. Inequalities for martingales indexed by [symbol]. 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. 5.7. Regression functions for processes -- 6. Inequalities for processes. 6.1. Introduction. 6.2. Stationary processes. 6.3. Ruin models. 6.4. Comparison of models. 6.5. Moments of the processes at T[symbol]. 6.6. Empirical process in mixture distributions. 6.7. Integral inequalities in the plane. 6.8. Spatial point processes -- 7. Inequalities in complex spaces. 7.1. Introduction. 7.2. Polynomials. 7.3. Fourier and Hermite transforms. 7.4. Inequalities for the transforms. 7.5. Inequalities in [symbol]. 7.6. Complex spaces of higher dimensions. 7.7. Stochastic integrals |
Beschreibung: | 1 Online-Ressource (232 pages) |
ISBN: | 1283900068 9781283900065 9789814412575 9789814412582 9814412570 9814412589 |
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500 | |a 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 generalizations. 2.6. Minkowski's inequality and generalizations. 2.7. Inequalities for the Laplace transform. 2.8. Inequalities for multivariate functions -- | ||
500 | |a - 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 variables. 4.3. Inequalities for discrete martingales. 4.4. Inequalities for martingales indexed by [symbol]. 4.5. Poisson processes. 4.6. Brownian motion. 4.7. Diffusion processes. 4.8. Level crossing probabilities. 4.9. Martingales in the plane -- | ||
500 | |a - 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. 5.7. Regression functions for processes -- 6. Inequalities for processes. 6.1. Introduction. 6.2. Stationary processes. 6.3. Ruin models. 6.4. Comparison of models. 6.5. Moments of the processes at T[symbol]. 6.6. Empirical process in mixture distributions. 6.7. Integral inequalities in the plane. 6.8. Spatial point processes -- 7. Inequalities in complex spaces. 7.1. Introduction. 7.2. Polynomials. 7.3. Fourier and Hermite transforms. 7.4. Inequalities for the transforms. 7.5. Inequalities in [symbol]. 7.6. Complex spaces of higher dimensions. 7.7. Stochastic integrals | ||
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Datensatz im Suchindex
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any_adam_object | |
author | Pons, Odile |
author_facet | Pons, Odile |
author_role | aut |
author_sort | Pons, Odile |
author_variant | o p op |
building | Verbundindex |
bvnumber | BV043134411 |
collection | ZDB-4-EBA |
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dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 515 - Analysis |
dewey-raw | 515.26 |
dewey-search | 515.26 |
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discipline | Mathematik |
format | Electronic eBook |
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id | DE-604.BV043134411 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:18:30Z |
institution | BVB |
isbn | 1283900068 9781283900065 9789814412575 9789814412582 9814412570 9814412589 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028558602 |
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owner_facet | DE-1046 DE-1047 |
physical | 1 Online-Ressource (232 pages) |
psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
publishDate | 2012 |
publishDateSearch | 2012 |
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publisher | World Scientific |
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spelling | Pons, Odile Verfasser aut Inequalities in Analysis and Probability Singapore World Scientific 2012 1 Online-Ressource (232 pages) txt rdacontent c rdamedia cr 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 Includes bibliographical references and index 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 generalizations. 2.6. 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 variables. 4.3. Inequalities for discrete martingales. 4.4. Inequalities for martingales indexed by [symbol]. 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. 5.7. Regression functions for processes -- 6. Inequalities for processes. 6.1. Introduction. 6.2. Stationary processes. 6.3. Ruin models. 6.4. Comparison of models. 6.5. Moments of the processes at T[symbol]. 6.6. Empirical process in mixture distributions. 6.7. Integral inequalities in the plane. 6.8. Spatial point processes -- 7. Inequalities in complex spaces. 7.1. Introduction. 7.2. Polynomials. 7.3. Fourier and Hermite transforms. 7.4. Inequalities for the transforms. 7.5. Inequalities in [symbol]. 7.6. Complex spaces of higher dimensions. 7.7. Stochastic integrals Fractional calculus Mathematics Inequalities (Mathematics) fast MATHEMATICS / Infinity bisacsh Mathematik Inequalities (Mathematics) Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Analysis (DE-588)4001865-9 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 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=517019 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Pons, Odile Inequalities in Analysis and Probability Fractional calculus Mathematics Inequalities (Mathematics) fast MATHEMATICS / Infinity bisacsh Mathematik Inequalities (Mathematics) Integrationstheorie (DE-588)4138369-2 gnd Ungleichung (DE-588)4139098-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Analysis (DE-588)4001865-9 gnd |
subject_GND | (DE-588)4138369-2 (DE-588)4139098-2 (DE-588)4079013-7 (DE-588)4001865-9 |
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 |
title_fullStr | Inequalities in Analysis and Probability |
title_full_unstemmed | Inequalities in Analysis and Probability |
title_short | Inequalities in Analysis and Probability |
title_sort | inequalities in analysis and probability |
topic | Fractional calculus Mathematics Inequalities (Mathematics) fast MATHEMATICS / Infinity bisacsh Mathematik Inequalities (Mathematics) Integrationstheorie (DE-588)4138369-2 gnd Ungleichung (DE-588)4139098-2 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Analysis (DE-588)4001865-9 gnd |
topic_facet | Fractional calculus Mathematics Inequalities (Mathematics) MATHEMATICS / Infinity Mathematik Integrationstheorie Ungleichung Wahrscheinlichkeitstheorie Analysis |
url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=517019 |
work_keys_str_mv | AT ponsodile inequalitiesinanalysisandprobability |