skip to content
Convergence of Stochastic Processes Preview this item
ClosePreview this item
Checking...

Convergence of Stochastic Processes

Author: David Pollard
Publisher: New York, NY : Springer New York, 1984.
Series: Springer series in statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David Pollard
ISBN: 9781461252542 1461252547
OCLC Number: 852792462
Description: 1 online resource (215 pages).
Contents: I Functional on Stochastic Processes --
1. Stochastic Processes as Random Functions --
II Uniform Convergence of Empirical Measures --
1. Uniformity and Consistency --
2. Direct Approximation --
3. The Combinatorial Method --
4. Classes of Sets with Polynomial Discrimination --
5. Classes of Functions --
6. Rates of Convergence --
III Convergence in Distribution in Euclidean Spaces --
1. The Definition --
2. The Continuous Mapping Theorem --
3. Expectations of Smooth Functions --
4. The Central Limit Theorem --
5. Characteristic Functions --
6. Quantile Transformations and Almost Sure Representations --
IV Convergence in Distribution in Metric Spaces --
1. Measurability --
2. The Continuous Mapping Theorem --
3. Representation by Almost Surely Convergent Sequences --
4. Coupling --
5. Weakly Convergent Subsequences --
V The Uniform Metric on Spaces of Cadlag Functions --
1. Approximation of Stochastic Processes --
2. Empirical Processes --
3. Existence of Brownian Bridge and Brownian Motion --
4. Processes with Independent Increments --
5. Infinite Time Scales --
6. Functional of Brownian Motion and Brownian Bridge --
VI The Skorohod Metric on D(0,?) --
1. Properties of the Metric --
2. Convergence in Distribution --
VII Central Limit Theorems --
1. Stochastic Equicontinuity --
2. Chaining --
3. Gaussian Processes --
4. Random Covering Numbers --
5. Empirical Central Limit Theorems --
6. Restricted Chaining --
VIII Martingales --
1. A Central Limit Theorem for Martingale-Difference Arrays --
2. Continuous Time Martingales --
3. Estimation from Censored Data --
Appendix A Stochastic-Order Symbols --
Appendix B Exponential Inequalities --
Notes --
Problems --
Appendix C Measurability --
Notes --
Problems --
References --
Author Index.
Series Title: Springer series in statistics.
Responsibility: by David Pollard.
More information:

Abstract:

A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(1)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/852792462> # Convergence of Stochastic Processes
    a schema:MediaObject, schema:Book, schema:CreativeWork ;
    library:oclcnum "852792462" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/3371169#Place/new_york_ny> ; # New York, NY
    schema:about <http://dewey.info/class/519.5/e23/> ;
    schema:about <http://id.worldcat.org/fast/1132103> ; # Statistics
    schema:bookFormat schema:EBook ;
    schema:creator <http://experiment.worldcat.org/entity/work/data/3371169#Person/pollard_david> ; # David Pollard
    schema:datePublished "1984" ;
    schema:description "A more accurate title for this book might be: An Exposition of Selected Parts of Empirical Process Theory, With Related Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. The high points are Chapters II and VII, which describe some of the developments inspired by Richard Dudley's 1978 paper. There I explain the combinatorial ideas and approximation methods that are needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions. The material is somewhat arbitrarily divided into results used to prove consistency theorems and results used to prove central limit theorems. This has allowed me to put the easier material in Chapter II, with the hope of enticing the casual reader to delve deeper. Chapters III through VI deal with more classical material, as seen from a different perspective. The novelties are: convergence for measures that don't live on borel a-fields; the joys of working with the uniform metric on D[O, IJ; and finite-dimensional approximation as the unifying idea behind weak convergence. Uniform tightness reappears in disguise as a condition that justifies the finite-dimensional approximation. Only later is it exploited as a method for proving the existence of limit distributions. The last chapter has a heuristic flavor. I didn't want to confuse the martingale issues with the martingale facts."@en ;
    schema:description "I Functional on Stochastic Processes -- 1. Stochastic Processes as Random Functions -- II Uniform Convergence of Empirical Measures -- 1. Uniformity and Consistency -- 2. Direct Approximation -- 3. The Combinatorial Method -- 4. Classes of Sets with Polynomial Discrimination -- 5. Classes of Functions -- 6. Rates of Convergence -- III Convergence in Distribution in Euclidean Spaces -- 1. The Definition -- 2. The Continuous Mapping Theorem -- 3. Expectations of Smooth Functions -- 4. The Central Limit Theorem -- 5. Characteristic Functions -- 6. Quantile Transformations and Almost Sure Representations -- IV Convergence in Distribution in Metric Spaces -- 1. Measurability -- 2. The Continuous Mapping Theorem -- 3. Representation by Almost Surely Convergent Sequences -- 4. Coupling -- 5. Weakly Convergent Subsequences -- V The Uniform Metric on Spaces of Cadlag Functions -- 1. Approximation of Stochastic Processes -- 2. Empirical Processes -- 3. Existence of Brownian Bridge and Brownian Motion -- 4. Processes with Independent Increments -- 5. Infinite Time Scales -- 6. Functional of Brownian Motion and Brownian Bridge -- VI The Skorohod Metric on D(0,?) -- 1. Properties of the Metric -- 2. Convergence in Distribution -- VII Central Limit Theorems -- 1. Stochastic Equicontinuity -- 2. Chaining -- 3. Gaussian Processes -- 4. Random Covering Numbers -- 5. Empirical Central Limit Theorems -- 6. Restricted Chaining -- VIII Martingales -- 1. A Central Limit Theorem for Martingale-Difference Arrays -- 2. Continuous Time Martingales -- 3. Estimation from Censored Data -- Appendix A Stochastic-Order Symbols -- Appendix B Exponential Inequalities -- Notes -- Problems -- Appendix C Measurability -- Notes -- Problems -- References -- Author Index."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/3371169> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/3371169#Series/springer_series_in_statistics> ; # Springer series in statistics.
    schema:isPartOf <http://worldcat.org/issn/0172-7397> ; # Springer Series in Statistics,
    schema:isSimilarTo <http://worldcat.org/entity/work/data/3371169#CreativeWork/> ;
    schema:name "Convergence of Stochastic Processes"@en ;
    schema:productID "852792462" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/852792462#PublicationEvent/new_york_ny_springer_new_york_1984> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/3371169#Agent/springer_new_york> ; # Springer New York
    schema:url <http://dx.doi.org/10.1007/978-1-4612-5254-2> ;
    schema:workExample <http://worldcat.org/isbn/9781461252542> ;
    schema:workExample <http://dx.doi.org/10.1007/978-1-4612-5254-2> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/852792462> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/3371169#Agent/springer_new_york> # Springer New York
    a bgn:Agent ;
    schema:name "Springer New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/3371169#Person/pollard_david> # David Pollard
    a schema:Person ;
    schema:familyName "Pollard" ;
    schema:givenName "David" ;
    schema:name "David Pollard" ;
    .

<http://experiment.worldcat.org/entity/work/data/3371169#Place/new_york_ny> # New York, NY
    a schema:Place ;
    schema:name "New York, NY" ;
    .

<http://experiment.worldcat.org/entity/work/data/3371169#Series/springer_series_in_statistics> # Springer series in statistics.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/852792462> ; # Convergence of Stochastic Processes
    schema:name "Springer series in statistics." ;
    .

<http://id.worldcat.org/fast/1132103> # Statistics
    a schema:Intangible ;
    schema:name "Statistics"@en ;
    .

<http://worldcat.org/entity/work/data/3371169#CreativeWork/>
    a schema:CreativeWork ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/852792462> ; # Convergence of Stochastic Processes
    .

<http://worldcat.org/isbn/9781461252542>
    a schema:ProductModel ;
    schema:isbn "1461252547" ;
    schema:isbn "9781461252542" ;
    .

<http://worldcat.org/issn/0172-7397> # Springer Series in Statistics,
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/852792462> ; # Convergence of Stochastic Processes
    schema:issn "0172-7397" ;
    schema:name "Springer Series in Statistics," ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.