Continuous martingales and Brownian motion:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Ausgabe: | 3. ed., corrected 3. print. |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
293 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XI, 606 S. |
| ISBN: | 3540643257 9783642084003 |
Internformat
MARC
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| 100 | 1 | |a Revuz, Daniel |d 1936- |e Verfasser |0 (DE-588)120628619 |4 aut | |
| 245 | 1 | 0 | |a Continuous martingales and Brownian motion |c Daniel Revuz ; Marc Yor |
| 250 | |a 3. ed., corrected 3. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XI, 606 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Die Grundlehren der mathematischen Wissenschaften |v 293 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Análise estocastica |2 larpcal | |
| 650 | 7 | |a Martingais |2 larpcal | |
| 650 | 7 | |a Processos de difusão |2 larpcal | |
| 650 | 4 | |a Brownian motion processes | |
| 650 | 4 | |a Martingales (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804135116102959104 |
|---|---|
| adam_text | Table
of
Contents
Chapter
0.
Preliminaries
................................................ 1
§1.
Basic Notation
..................................................... 1
§2.
Monotone Class Theorem
.......................................... 2
§3.
Completion
........................................................ 3
§4.
Functions of Finite Variation and
Stieltjes
Integrals
................... 4
§5.
Weak Convergence in Metric Spaces
................................ 9
§6.
Gaussian and Other Random Variables
............................... 11
Chapter I. Introduction
................................................. 15
§1.
Examples of Stochastic Processes. Brownian Motion
.................. 15
§2.
Local Properties of Brownian Paths
................................. 26
§3.
Canonical Processes and Gaussian Processes
......................... 33
§4.
Filtrations and Stopping Times
...................................... 41
Notes and Comments
.................................................. 48
Chapter II. Martingales
................................................ 51
§ 1.
Definitions, Maximal Inequalities and Applications
................... 51
§2.
Convergence and Regularization Theorems
........................... 60
§3.
Optional Stopping Theorem
......................................... 68
Notes and Comments
.................................................. 77
Chapter III. Markov Processes
.......................................... 79
§1.
Basic Definitions
................................................... 79
§2.
Feller Processes
.................................................... 88
§3.
Strong Markov Property
............................,............... 102
§4.
Summary of Results on Levy Processes
.............................. 114
Notes and Comments
.................................................. 117
Chapter IV. Stochastic Integration
...................................... 119
§ 1.
Quadratic Variations
................................................ 119
§2.
Stochastic Integrals
................................................ 137
§3.
Itô s Formula and First Applications
................................. 146
§4.
Burkholder-Davis-Gundy
Inequalities
................................ 160
§5.
Predictable Processes
............................................... 171
Notes
and Comments
.................................................. 176
Chapter V. Representation of Martingales
............................... 179
§1.
Continuous Martingales as Time-changed Brownian Motions
.......... 179
§2.
Conformai
Martingales and Planar Brownian Motion
................. 189
§3.
Brownian Martingales
.............................................. 198
§4.
Integral Representations
............................................ 209
Notes and Comments
.................................................. 216
Chapter VI. Local Times
............................................... 221
§1.
Definition and First Properties
...................................... 221
§2.
The Local Time of Brownian Motion
................................ 239
§3.
The Three-Dimensional Bessel Process
.............................. 251
§4.
First Order Calculus
................................................260
§5.
The Skorokhod Stopping Problem
................................... 269
Notes and Comments
.................................................. 277
Chapter
VII.
Generators and Time Reversal
............................. 281
§ 1.
Infinitesimal Generators
............................................ 281
§2.
Diffusions and
Ito
Processes
........................................ 294
§3.
Linear Continuous Markov Processes
................................ 300
§4.
Time Reversal and Applications
.....................................313
Notes and Comments
.................................................. 322
Chapter
VIII.
Girsanov s Theorem and First Applications
................. 325
§1.
Girsanov s Theorem
................................................325
§2.
Application of Girsanov s Theorem to the Study of Wiener s Space
___338
§3.
Functionals and Transformations of Diffusion Processes
...............349
Notes and Comments
.................................................. 362
Chapter IX. Stochastic Differential Equations
........................___ 365
§ 1.
Formal Definitions and Uniqueness
..................................365
§2.
Existence and Uniqueness in the Case of Lipschitz Coefficients
........375
§3.
The Case of Holder Coefficients in Dimension One
...................388
Notes and Comments
.................................................. 399
Chapter X. Additive Functionals of Brownian Motion
.................... 401
§1.
General Definitions
................................................ 401
§2.
Representation Theorem for Additive Functionals
of Linear Brownian Motion
.........................................409
§3.
Ergodic Theorems for Additive Functionals
.......................... 422
§4.
Asymptotic Results for the Planar Brownian Motion
.................. 430
Notes and Comments
.................................................. 436
Chapter XI. Bessel Processes and Ray-Knight Theorems
..................439
§1.
Bessel Processes
................................................... 439
§2.
Ray-Knight Theorems
.............................................. 454
§3.
Bessel Bridges
.....................................................463
Notes and Comments
.................................................. 469
Chapter
XII.
Excursions
................................................471
§1.
Prerequisites on
Poisson
Point Processes
............................. 471
§2.
The Excursion Process of Brownian Motion
.......................... 480
§3.
Excursions Straddling a Given Time
................................. 488
§4.
Descriptions of
Itô s
Measure and Applications
...................... 493
Notes and Comments
.................................................. 511
Chapter
XIII.
Limit Theorems in Distribution
............................ 515
§1.
Convergence in Distribution
........................................ 515
§2.
Asymptotic Behavior of Additive Functionals of Brownian Motion
___ 522
§3.
Asymptotic Properties of Planar Brownian Motion
.................... 531
Notes and Comments
.................................................. 541
Appendix
............................................................. 543
§ 1.
Gronwall s Lemma
................................................. 543
§2.
Distributions
....................................................... 543
§3.
Convex Functions
.................................................. 544
§4.
Hausdorff Measures and Dimension
................................. 547
§5.
Ergodic Theory
.................................................... 548
§6.
Probabilities on Function Spaces
.................................... 548
§7.
Bessel Functions
................................................... 549
§8.
Sturm-Liouville Equation
........................................... 550
Bibliography
.......................................................... 553
Index of Notation
..................................................... 595
Index of Terms
........................................................ 599
Catalogue
............................................................. 605
|
| adam_txt |
Table
of
Contents
Chapter
0.
Preliminaries
. 1
§1.
Basic Notation
. 1
§2.
Monotone Class Theorem
. 2
§3.
Completion
. 3
§4.
Functions of Finite Variation and
Stieltjes
Integrals
. 4
§5.
Weak Convergence in Metric Spaces
. 9
§6.
Gaussian and Other Random Variables
. 11
Chapter I. Introduction
. 15
§1.
Examples of Stochastic Processes. Brownian Motion
. 15
§2.
Local Properties of Brownian Paths
. 26
§3.
Canonical Processes and Gaussian Processes
. 33
§4.
Filtrations and Stopping Times
. 41
Notes and Comments
. 48
Chapter II. Martingales
. 51
§ 1.
Definitions, Maximal Inequalities and Applications
. 51
§2.
Convergence and Regularization Theorems
. 60
§3.
Optional Stopping Theorem
. 68
Notes and Comments
. 77
Chapter III. Markov Processes
. 79
§1.
Basic Definitions
. 79
§2.
Feller Processes
. 88
§3.
Strong Markov Property
.,. 102
§4.
Summary of Results on Levy Processes
. 114
Notes and Comments
. 117
Chapter IV. Stochastic Integration
. 119
§ 1.
Quadratic Variations
. 119
§2.
Stochastic Integrals
. 137
§3.
Itô's Formula and First Applications
. 146
§4.
Burkholder-Davis-Gundy
Inequalities
. 160
§5.
Predictable Processes
. 171
Notes
and Comments
. 176
Chapter V. Representation of Martingales
. 179
§1.
Continuous Martingales as Time-changed Brownian Motions
. 179
§2.
Conformai
Martingales and Planar Brownian Motion
. 189
§3.
Brownian Martingales
. 198
§4.
Integral Representations
. 209
Notes and Comments
. 216
Chapter VI. Local Times
. 221
§1.
Definition and First Properties
. 221
§2.
The Local Time of Brownian Motion
. 239
§3.
The Three-Dimensional Bessel Process
. 251
§4.
First Order Calculus
.260
§5.
The Skorokhod Stopping Problem
. 269
Notes and Comments
. 277
Chapter
VII.
Generators and Time Reversal
. 281
§ 1.
Infinitesimal Generators
. 281
§2.
Diffusions and
Ito
Processes
. 294
§3.
Linear Continuous Markov Processes
. 300
§4.
Time Reversal and Applications
.313
Notes and Comments
. 322
Chapter
VIII.
Girsanov's Theorem and First Applications
. 325
§1.
Girsanov's Theorem
.325
§2.
Application of Girsanov's Theorem to the Study of Wiener's Space
_338
§3.
Functionals and Transformations of Diffusion Processes
.349
Notes and Comments
. 362
Chapter IX. Stochastic Differential Equations
._ 365
§ 1.
Formal Definitions and Uniqueness
.365
§2.
Existence and Uniqueness in the Case of Lipschitz Coefficients
.375
§3.
The Case of Holder Coefficients in Dimension One
.388
Notes and Comments
. 399
Chapter X. Additive Functionals of Brownian Motion
. 401
§1.
General Definitions
. 401
§2.
Representation Theorem for Additive Functionals
of Linear Brownian Motion
.409
§3.
Ergodic Theorems for Additive Functionals
. 422
§4.
Asymptotic Results for the Planar Brownian Motion
. 430
Notes and Comments
. 436
Chapter XI. Bessel Processes and Ray-Knight Theorems
.439
§1.
Bessel Processes
. 439
§2.
Ray-Knight Theorems
. 454
§3.
Bessel Bridges
.463
Notes and Comments
. 469
Chapter
XII.
Excursions
.471
§1.
Prerequisites on
Poisson
Point Processes
. 471
§2.
The Excursion Process of Brownian Motion
. 480
§3.
Excursions Straddling a Given Time
. 488
§4.
Descriptions of
Itô's
Measure and Applications
. 493
Notes and Comments
. 511
Chapter
XIII.
Limit Theorems in Distribution
. 515
§1.
Convergence in Distribution
. 515
§2.
Asymptotic Behavior of Additive Functionals of Brownian Motion
_ 522
§3.
Asymptotic Properties of Planar Brownian Motion
. 531
Notes and Comments
. 541
Appendix
. 543
§ 1.
Gronwall's Lemma
. 543
§2.
Distributions
. 543
§3.
Convex Functions
. 544
§4.
Hausdorff Measures and Dimension
. 547
§5.
Ergodic Theory
. 548
§6.
Probabilities on Function Spaces
. 548
§7.
Bessel Functions
. 549
§8.
Sturm-Liouville Equation
. 550
Bibliography
. 553
Index of Notation
. 595
Index of Terms
. 599
Catalogue
. 605 |
| any_adam_object | 1 |
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| author | Revuz, Daniel 1936- Yor, Marc 1949-2014 |
| author_GND | (DE-588)120628619 (DE-588)120628635 |
| author_facet | Revuz, Daniel 1936- Yor, Marc 1949-2014 |
| author_role | aut aut |
| author_sort | Revuz, Daniel 1936- |
| author_variant | d r dr m y my |
| building | Verbundindex |
| bvnumber | BV021311965 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.5 |
| callnumber-search | QA274.5 |
| callnumber-sort | QA 3274.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)61730370 (DE-599)BVBBV021311965 |
| dewey-full | 519.236 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.236 |
| dewey-search | 519.236 |
| dewey-sort | 3519.236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed., corrected 3. print. |
| format | Book |
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| id | DE-604.BV021311965 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:56:17Z |
| indexdate | 2024-07-09T20:35:23Z |
| institution | BVB |
| isbn | 3540643257 9783642084003 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014632515 |
| oclc_num | 61730370 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29T DE-739 DE-91G DE-BY-TUM DE-11 DE-83 DE-92 DE-188 DE-523 DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-29T DE-739 DE-91G DE-BY-TUM DE-11 DE-83 DE-92 DE-188 DE-523 DE-20 |
| physical | XI, 606 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spelling | Revuz, Daniel 1936- Verfasser (DE-588)120628619 aut Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor 3. ed., corrected 3. print. Berlin [u.a.] Springer 2005 XI, 606 S. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 293 Hier auch später erschienene, unveränderte Nachdrucke Análise estocastica larpcal Martingais larpcal Processos de difusão larpcal Brownian motion processes Martingales (Mathematics) Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Martingaltheorie (DE-588)4168982-3 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Martingal (DE-588)4126466-6 s DE-604 Stochastische Analysis (DE-588)4132272-1 s Martingaltheorie (DE-588)4168982-3 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Yor, Marc 1949-2014 Verfasser (DE-588)120628635 aut Die Grundlehren der mathematischen Wissenschaften 293 (DE-604)BV000000395 293 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014632515&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 | Revuz, Daniel 1936- Yor, Marc 1949-2014 Continuous martingales and Brownian motion Die Grundlehren der mathematischen Wissenschaften Análise estocastica larpcal Martingais larpcal Processos de difusão larpcal Brownian motion processes Martingales (Mathematics) Stochastischer Prozess (DE-588)4057630-9 gnd Martingal (DE-588)4126466-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingaltheorie (DE-588)4168982-3 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4126466-6 (DE-588)4128328-4 (DE-588)4168982-3 (DE-588)4132272-1 |
| title | Continuous martingales and Brownian motion |
| title_auth | Continuous martingales and Brownian motion |
| title_exact_search | Continuous martingales and Brownian motion |
| title_exact_search_txtP | Continuous martingales and Brownian motion |
| title_full | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_fullStr | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_full_unstemmed | Continuous martingales and Brownian motion Daniel Revuz ; Marc Yor |
| title_short | Continuous martingales and Brownian motion |
| title_sort | continuous martingales and brownian motion |
| topic | Análise estocastica larpcal Martingais larpcal Processos de difusão larpcal Brownian motion processes Martingales (Mathematics) Stochastischer Prozess (DE-588)4057630-9 gnd Martingal (DE-588)4126466-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Martingaltheorie (DE-588)4168982-3 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Análise estocastica Martingais Processos de difusão Brownian motion processes Martingales (Mathematics) Stochastischer Prozess Martingal Brownsche Bewegung Martingaltheorie Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014632515&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT revuzdaniel continuousmartingalesandbrownianmotion AT yormarc continuousmartingalesandbrownianmotion |