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 ItoNisio theorem  3.2 Fourier expansion and construction of Brownian motion  3.3 Symmetric Levy measures and generalized Poisson measures  3.4 The LevyKhinchin 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 evyKhinchin 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 SturmLiouville 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 algebraictopological 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 indepth 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 algebraictopological 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 SturmLiouville hypergroups, and on the central limit problem for groups such as tori, padic 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

