Continuous martingales and Brownian motion:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
293 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 602 S. |
| ISBN: | 3540643257 |
Internformat
MARC
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| 245 | 1 | 0 | |a Continuous martingales and Brownian motion |c Daniel Revuz ; Marc Yor |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIII, 602 S. | ||
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| 650 | 0 | 7 | |a Martingaltheorie |0 (DE-588)4168982-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804126955508858880 |
|---|---|
| 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
XII Table of Contents
§3. Ito 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. Conformal 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 238
§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 293
§3. Linear Continuous Markov Processes 300
§4. Time Reversal and Applications 312
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
Table of Contents XIII
§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 Ito 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 591
Index of Terms 595
Catalogue 601
|
| any_adam_object | 1 |
| 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 | BV012329087 |
| classification_rvk | QH 234 SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)40481166 (DE-599)BVBBV012329087 |
| dewey-full | 519.287 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.287 |
| dewey-search | 519.287 |
| dewey-sort | 3519.287 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV012329087 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:25:40Z |
| institution | BVB |
| isbn | 3540643257 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008359796 |
| oclc_num | 40481166 |
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| physical | XIII, 602 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| 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. Berlin [u.a.] Springer 1999 XIII, 602 S. txt rdacontent n rdamedia nc rdacarrier Die Grundlehren der mathematischen Wissenschaften 293 Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf 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 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359796&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 Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd 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 |
| subject_GND | (DE-588)4132272-1 (DE-588)4057630-9 (DE-588)4126466-6 (DE-588)4128328-4 (DE-588)4168982-3 |
| title | Continuous martingales and Brownian motion |
| title_auth | Continuous martingales and Brownian motion |
| title_exact_search | 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 | Brownian motion processes Martingales (Mathematics) Stochastische Analysis (DE-588)4132272-1 gnd 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 |
| topic_facet | Brownian motion processes Martingales (Mathematics) Stochastische Analysis Stochastischer Prozess Martingal Brownsche Bewegung Martingaltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008359796&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 |