The Resource Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)
Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/)
Resource Information
The item Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Old Colony Library Network.This item is available to borrow from 2 library branches.
Resource Information
The item Structural aspects in the theory of probability, Herbert Heyer, (electronic resource/) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Old Colony Library Network.
This item is available to borrow from 2 library branches.
 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 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 wit
 Language
 eng
 Edition

 2nd enl. ed. /
 with an additional chapter by Gyula Pap.
 Extent
 1 online resource (access may be restricted)
 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 ItoNisio theorem; 3.2 Fourier expansion and construction of Brownian motion
 3.3 Symmetric Levy measures and generalized Poisson measures3.4 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 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 SturmLiouville 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
 Label
 Structural aspects in the theory of probability
 Title
 Structural aspects in the theory of probability
 Statement of responsibility
 Herbert Heyer
 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 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 wit
 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/)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 389395) 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 ItoNisio theorem; 3.2 Fourier expansion and construction of Brownian motion
 3.3 Symmetric Levy measures and generalized Poisson measures3.4 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 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 SturmLiouville 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/)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 389395) 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 ItoNisio theorem; 3.2 Fourier expansion and construction of Brownian motion
 3.3 Symmetric Levy measures and generalized Poisson measures3.4 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 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 SturmLiouville 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
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