Description

Book Synopsis
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.

Table of Contents
Classical Probability Inequalities; Burkholder Inequality; Cauchy Inequalities; Chernov Theorem; Donsker Classes; Martingales; Brownian Motion; Empirical Process; Solutions of Diffusion Equations; Complex Spaces; Fourier Transform; Hermite Polynomials; Laplace Transform; Tightness; Weak Convergence.

Inequalities In Analysis And Probability

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    A Hardback by Odile Pons

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      View other formats and editions of Inequalities In Analysis And Probability by Odile Pons

      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: 22/01/2013
      ISBN13: 9789814412575, 978-9814412575
      ISBN10: 9814412570

      Description

      Book Synopsis
      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.

      Table of Contents
      Classical Probability Inequalities; Burkholder Inequality; Cauchy Inequalities; Chernov Theorem; Donsker Classes; Martingales; Brownian Motion; Empirical Process; Solutions of Diffusion Equations; Complex Spaces; Fourier Transform; Hermite Polynomials; Laplace Transform; Tightness; Weak Convergence.

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