Functional analysis for probability and stochastic processes: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York
Cambridge University Press
2007
|
| Ausgabe: | Reprinted with corrections |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 393 Seiten |
| ISBN: | 9780521539371 9780521831666 0521539374 |
Internformat
MARC
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| 100 | 1 | |a Bobrowski, Adam |d ca. 20./21. Jh. |0 (DE-588)141939656 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis for probability and stochastic processes |b an introduction |
| 250 | |a Reprinted with corrections | ||
| 264 | 1 | |a Cambridge ; New York |b Cambridge University Press |c 2007 | |
| 300 | |a xii, 393 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Funktionalanalysis - Stochastischer Prozess - Wahrscheinlichkeitstheorie | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Functional analysis |v Problems, exercises, etc | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Stochastic processes | |
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| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804138054416334848 |
|---|---|
| adam_text | Contents
Preface
page
xi
1
Preliminaries, notations and conventions
1
1.1
Elements of topology
1
1.2
Measure theory
3
1.3
Functions of bounded variation. Riemann-Stieltjes integral
17
1.4
Sequences of independent random variables
23
1.5
Convex functions. Holder and Minkowski inequalities
29
1.6
The Cauchy equation
33
2
Basic notions in functional analysis
37
2.1
Linear spaces
37
2.2
Banach spaces
44
2.3
The space of bounded linear operators
63
3
Conditional expectation
80
3.1
Projections in Hubert spaces
80
3.2
Definition and existence of conditional expectation
87
3.3
Properties and examples
91
3.4
The Radon-Nikodym Theorem
101
3.5
Examples of discrete martingales
103
3.6
Convergence of self-adjoint operators
106
3.7 ...
and of martingales
112
4
Brownian motion and Hubert spaces
121
4.1
Gaussian families
&
the definition of Brownian motion
123
4.2
Complete
orthonormal
sequences in a Hubert space
127
4.3
Construction
and basic properties of Brownian motion
4.4
Stochastic integrals
5
Dual spaces and convergence of probability measures
5.1
The Hahn-Banach Theorem
5.2
Form of linear functionals in specific Banach spaces
5.3
The dual of an operator
5.4
Weak and weak* topologies
5.5
The Central Limit Theorem
5.6
Weak convergence in metric spaces
5.7
Compactness everywhere
5.8
Notes on other modes of convergence
6
The Gelfand transform and its applications
6.1
Banach algebras
6.2
The Gelfand transform
6.3
Examples of Gelfand transform
6.4
Examples of explicit calculations of Gelfand transform
6.5
Dense subalgebras of C(S)
6.6
Inverting the abstract Fourier transform
6.7
The Factorization Theorem
7
Semigroups of operators and Levy processes
7.1
The Banach-Steinhaus Theorem
7.2
Calculus of Banach space valued functions
7.3
Closed operators
7.4
Semigroups of operators
7.5
Brownian motion and
Poisson
process semigroups
7.6
More convolution semigroups
7.7
The telegraph process semigroup
7.8
Convolution semigroups of measures on semigroups
8
Markov processes and semigroups of operators
8.1
Semigroups of operators related to Markov processes
8.2
The Hille-Yosida Theorem
8.3
Generators of stochastic processes
8.4
Approximation theorems
9
Appendixes
363
9.1
Bibliographical notes
363
Contents ix
9.2 Solutions
and hints to exercises
366
9.3
Some commonly used notations
383
References
385
Index
390
|
| adam_txt |
Contents
Preface
page
xi
1
Preliminaries, notations and conventions
1
1.1
Elements of topology
1
1.2
Measure theory
3
1.3
Functions of bounded variation. Riemann-Stieltjes integral
17
1.4
Sequences of independent random variables
23
1.5
Convex functions. Holder and Minkowski inequalities
29
1.6
The Cauchy equation
33
2
Basic notions in functional analysis
37
2.1
Linear spaces
37
2.2
Banach spaces
44
2.3
The space of bounded linear operators
63
3
Conditional expectation
80
3.1
Projections in Hubert spaces
80
3.2
Definition and existence of conditional expectation
87
3.3
Properties and examples
91
3.4
The Radon-Nikodym Theorem
101
3.5
Examples of discrete martingales
103
3.6
Convergence of self-adjoint operators
106
3.7 .
and of martingales
112
4
Brownian motion and Hubert spaces
121
4.1
Gaussian families
&
the definition of Brownian motion
123
4.2
Complete
orthonormal
sequences in a Hubert space
127
4.3
Construction
and basic properties of Brownian motion
4.4
Stochastic integrals
5
Dual spaces and convergence of probability measures
5.1
The Hahn-Banach Theorem
5.2
Form of linear functionals in specific Banach spaces
5.3
The dual of an operator
5.4
Weak and weak* topologies
5.5
The Central Limit Theorem
5.6
Weak convergence in metric spaces
5.7
Compactness everywhere
5.8
Notes on other modes of convergence
6
The Gelfand transform and its applications
6.1
Banach algebras
6.2
The Gelfand transform
6.3
Examples of Gelfand transform
6.4
Examples of explicit calculations of Gelfand transform
6.5
Dense subalgebras of C(S)
6.6
Inverting the abstract Fourier transform
6.7
The Factorization Theorem
7
Semigroups of operators and Levy processes
7.1
The Banach-Steinhaus Theorem
7.2
Calculus of Banach space valued functions
7.3
Closed operators
7.4
Semigroups of operators
7.5
Brownian motion and
Poisson
process semigroups
7.6
More convolution semigroups
7.7
The telegraph process semigroup
7.8
Convolution semigroups of measures on semigroups
8
Markov processes and semigroups of operators
8.1
Semigroups of operators related to Markov processes
8.2
The Hille-Yosida Theorem
8.3
Generators of stochastic processes
8.4
Approximation theorems
9
Appendixes
363
9.1
Bibliographical notes
363
Contents ix
9.2 Solutions
and hints to exercises
366
9.3
Some commonly used notations
383
References
385
Index
390 |
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| author | Bobrowski, Adam ca. 20./21. Jh |
| author_GND | (DE-588)141939656 |
| author_facet | Bobrowski, Adam ca. 20./21. Jh |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Reprinted with corrections |
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| spelling | Bobrowski, Adam ca. 20./21. Jh. (DE-588)141939656 aut Functional analysis for probability and stochastic processes an introduction Reprinted with corrections Cambridge ; New York Cambridge University Press 2007 xii, 393 Seiten txt rdacontent n rdamedia nc rdacarrier Funktionalanalysis - Stochastischer Prozess - Wahrscheinlichkeitstheorie Functional analysis Functional analysis Problems, exercises, etc Probabilities Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Stochastischer Prozess (DE-588)4057630-9 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016763336&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bobrowski, Adam ca. 20./21. Jh Functional analysis for probability and stochastic processes an introduction Funktionalanalysis - Stochastischer Prozess - Wahrscheinlichkeitstheorie Functional analysis Functional analysis Problems, exercises, etc Probabilities Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4018916-8 (DE-588)4079013-7 (DE-588)4064324-4 |
| title | Functional analysis for probability and stochastic processes an introduction |
| title_auth | Functional analysis for probability and stochastic processes an introduction |
| title_exact_search | Functional analysis for probability and stochastic processes an introduction |
| title_exact_search_txtP | Functional analysis for probability and stochastic processes an introduction |
| title_full | Functional analysis for probability and stochastic processes an introduction |
| title_fullStr | Functional analysis for probability and stochastic processes an introduction |
| title_full_unstemmed | Functional analysis for probability and stochastic processes an introduction |
| title_short | Functional analysis for probability and stochastic processes |
| title_sort | functional analysis for probability and stochastic processes an introduction |
| title_sub | an introduction |
| topic | Funktionalanalysis - Stochastischer Prozess - Wahrscheinlichkeitstheorie Functional analysis Functional analysis Problems, exercises, etc Probabilities Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd Funktionalanalysis (DE-588)4018916-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Funktionalanalysis - Stochastischer Prozess - Wahrscheinlichkeitstheorie Functional analysis Functional analysis Problems, exercises, etc Probabilities Stochastic processes Stochastischer Prozess Funktionalanalysis Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016763336&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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