作者 Heyer, Herbert
書名 Structural Aspects in the Theory of Probability
出版項 Singapore : World Scientific Publishing Co Pte Ltd, 2009
©2009
國際標準書號 9789814282499 (electronic bk.)
9789814282482
book jacket
版本 2nd ed
說明 1 online resource (425 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 World Scientific Series In Nanoscience And Nanotechnology ; v.8
World Scientific Series In Nanoscience And Nanotechnology
附註 Intro -- Contents -- Preface to the second enlarged edition -- Preface -- 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 measures -- 3.4 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 criterion -- 6.3 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 hypergroup -- Comments 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 with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm-Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids. Sample Chapter(s). Chapter 1: Probability Measures on Metric Spaces (318 KB). Contents: Probability Measures on Metric Spaces; The Fourier Transform in a Banach Space; The Structure of Infinitely Divisible Probability Measures; Harmonic Analysis of Convolution Semigroups; Negative Definite Functions and Convolution Semigroups; Probabilistic Properties of Convolution Semigroups; Hypergroups in Probability Theory; Limit Theorems on Locally Compact Abelian Groups. Readership: Graduate students, lecturers and researchers in probability and statistics
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Heyer, Herbert Structural Aspects in the Theory of Probability Singapore : World Scientific Publishing Co Pte Ltd,c2009 9789814282482
主題 Probabilities.;Topological groups.;Banach spaces.;Probability measures.;Abelian groups
Electronic books