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050 4 QA273.43 -- .H53 2009eb
082 0 519.2
100 1 Heyer, Herbert
245 10 Structural Aspects in the Theory of Probability
250 2nd ed
264 1 Singapore :|bWorld Scientific Publishing Co Pte Ltd,|c2009
264 4 |c©2009
300 1 online resource (425 pages)
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
490 1 World Scientific Series In Nanoscience And Nanotechnology
;|vv.8
505 0 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
505 8 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
520 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
588 Description based on publisher supplied metadata and other
sources
590 Electronic reproduction. Ann Arbor, Michigan : ProQuest
Ebook Central, 2020. Available via World Wide Web. Access
may be limited to ProQuest Ebook Central affiliated
libraries
650 0 Probabilities.;Topological groups.;Banach
spaces.;Probability measures.;Abelian groups
655 4 Electronic books
776 08 |iPrint version:|aHeyer, Herbert|tStructural Aspects in
the Theory of Probability|dSingapore : World Scientific
Publishing Co Pte Ltd,c2009|z9789814282482
830 0 World Scientific Series In Nanoscience And Nanotechnology
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
detail.action?docID=1679582|zClick to View