The Resource Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)

Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)

Label
Structural aspects in the theory of probability
Title
Structural aspects in the theory of probability
Statement of responsibility
Herbert Heyer
Creator
Contributor
Subject
Genre
Language
eng
Summary
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 wit
Related
Member of
Cataloging source
N$T
Dewey number
519.2
Index
index present
LC call number
QA273.43
LC item number
.H53 2010eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Series on multivariate analysis
Series volume
v. 8
Label
Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)
Link
http://library.quincycollege.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340559
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 389-395) and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface to the second enlarged edition; Preface; Contents; 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 measures3.4 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 criterion6.3 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 hypergroupComments 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 Gaisers 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
Control code
ocn696139086
Dimensions
unknown
Edition
  • 2nd enl. ed. /
  • with an additional chapter by Gyula Pap.
Extent
1 online resource (access may be restricted)
File format
unknown
Form of item
online
Governing access note
Access restricted to subscribing institution
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
  • eBooks on EBSCOhost
  • eBooks on EBSCOhost
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Label
Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)
Link
http://library.quincycollege.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340559
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 389-395) and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface to the second enlarged edition; Preface; Contents; 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 measures3.4 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 criterion6.3 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 hypergroupComments 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 Gaisers 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
Control code
ocn696139086
Dimensions
unknown
Edition
  • 2nd enl. ed. /
  • with an additional chapter by Gyula Pap.
Extent
1 online resource (access may be restricted)
File format
unknown
Form of item
online
Governing access note
Access restricted to subscribing institution
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
  • eBooks on EBSCOhost
  • eBooks on EBSCOhost
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote

Library Locations

    • Massasoit Community College Brockton CampusBorrow it
      1 Massasoit Blvd., Brockton, MA, 02301, US
      42.07562679999999 -70.99027629999999
    • Nease Library - Eastern Nazarene College Borrow it
      23 East Elm Ave. , Quincy, MA, 02170, US
      42.271089 -71.012428
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