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Inequalities In Analysis And Probability (Third Edition)

Author: Odile Pons

Publisher: World Scientific

Published: 2021-10-18

Total Pages: 371

ISBN-13: 9811231362

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The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.

Book Synopsis Inequalities In Analysis And Probability (Third Edition) by : Odile Pons

Download or read book Inequalities In Analysis And Probability (Third Edition) written by Odile Pons and published by World Scientific. This book was released on 2021-10-18 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces classical inequalities in vector and functional spaces with applications to probability. It develops new analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales, to transformed Brownian motions and diffusions, to Markov and point processes, renewal, branching and shock processes.In this third edition, the inequalities for martingales are presented in two chapters for discrete and time-continuous local martingales with new results for the bound of the norms of a martingale by the norms of the predictable processes of its quadratic variations, for the norms of their supremum and their p-variations. More inequalities are also covered for the tail probabilities of Gaussian processes and for spatial processes.This book is well-suited for undergraduate and graduate students as well as researchers in theoretical and applied mathematics.

Inequalities in Analysis and Probability

Author: Odile Pons

Publisher: World Scientific

Published: 2016-11-03

Total Pages: 308

ISBN-13: 9813144009

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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 many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

Book Synopsis Inequalities in Analysis and Probability by : Odile Pons

Download or read book Inequalities in Analysis and Probability written by Odile Pons and published by World Scientific. This book was released on 2016-11-03 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane. This second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their p-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman–Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.

Concentration of Measure Inequalities in Information Theory, Communications, and Coding

Author: Maxim Raginsky

Publisher:

Published: 2014

Total Pages: 256

ISBN-13: 9781601989062

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Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.

Book Synopsis Concentration of Measure Inequalities in Information Theory, Communications, and Coding by : Maxim Raginsky

Download or read book Concentration of Measure Inequalities in Information Theory, Communications, and Coding written by Maxim Raginsky and published by . This book was released on 2014 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.

Inequalities In Analysis And Probability (Third Edition)

Author: Odile Pons

Publisher:

Published: 2021

Total Pages: 371

ISBN-13: 9789811231353

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"The book is complementary to the classical courses on vector and functional Hilbert spaces, integration theory and probability which focus on inequalities; The preliminary chapter introduces most classical inequalities which are generalized to more complex models with detailed proofs; It covers different domains from existing books and contains many new results; It gathers inequalities from several domains of mathematics which are not generally presented together, in a unified approach; The topics include many stochastic processes with specific inequalities and the basis of the stochastic calculus is developed in numerous applications"--

Book Synopsis Inequalities In Analysis And Probability (Third Edition) by : Odile Pons

Download or read book Inequalities In Analysis And Probability (Third Edition) written by Odile Pons and published by . This book was released on 2021 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is complementary to the classical courses on vector and functional Hilbert spaces, integration theory and probability which focus on inequalities; The preliminary chapter introduces most classical inequalities which are generalized to more complex models with detailed proofs; It covers different domains from existing books and contains many new results; It gathers inequalities from several domains of mathematics which are not generally presented together, in a unified approach; The topics include many stochastic processes with specific inequalities and the basis of the stochastic calculus is developed in numerous applications"--

Probability Inequalities

Author: Zhengyan Lin

Publisher: Springer Science & Business Media

Published: 2011-05-30

Total Pages: 192

ISBN-13: 3642052614

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Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.

Book Synopsis Probability Inequalities by : Zhengyan Lin

Download or read book Probability Inequalities written by Zhengyan Lin and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.

Analysis And Differential Equations (Second Edition)

Author: Odile Pons

Publisher: World Scientific

Published: 2022-12-19

Total Pages: 305

ISBN-13: 9811268584

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The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

Book Synopsis Analysis And Differential Equations (Second Edition) by : Odile Pons

Download or read book Analysis And Differential Equations (Second Edition) written by Odile Pons and published by World Scientific. This book was released on 2022-12-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

Inequalities in Statistics and Probability

Author: Yung Liang Tong

Publisher: IMS

Published: 1984

Total Pages: 270

ISBN-13: 9780940600041

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Book Synopsis Inequalities in Statistics and Probability by : Yung Liang Tong

Download or read book Inequalities in Statistics and Probability written by Yung Liang Tong and published by IMS. This book was released on 1984 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inequalities: A Journey into Linear Analysis

Author: D. J. H. Garling

Publisher: Cambridge University Press

Published: 2007-07-05

Total Pages: 347

ISBN-13: 1139465147

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This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

Book Synopsis Inequalities: A Journey into Linear Analysis by : D. J. H. Garling

Download or read book Inequalities: A Journey into Linear Analysis written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2007-07-05 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

Functional Estimation For Density, Regression Models And Processes (Second Edition)

Author: Odile Pons

Publisher: World Scientific

Published: 2023-09-22

Total Pages: 259

ISBN-13: 9811272859

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Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.

Book Synopsis Functional Estimation For Density, Regression Models And Processes (Second Edition) by : Odile Pons

Download or read book Functional Estimation For Density, Regression Models And Processes (Second Edition) written by Odile Pons and published by World Scientific. This book was released on 2023-09-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.

Probability and Measure

Author: Patrick Billingsley

Publisher: John Wiley & Sons

Published: 2017

Total Pages: 612

ISBN-13: 9788126517718

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Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

Book Synopsis Probability and Measure by : Patrick Billingsley

Download or read book Probability and Measure written by Patrick Billingsley and published by John Wiley & Sons. This book was released on 2017 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes