Stochastic integration and differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Applications of mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 389 - 401 |
| Beschreibung: | XIII, 415 S. |
| ISBN: | 3540003134 |
Internformat
MARC
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| 245 | 1 | 0 | |a Stochastic integration and differential equations |c Philip E. Protter |
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Datensatz im Suchindex
| _version_ | 1804129839394848768 |
|---|---|
| adam_text | PHILIP E. PROTTER INTEGRATION S AND DIFFERENTIAL EQUATIONS SECOND
EDITION SPRINGER CONTENTS INTRODUCTION 1 I PRELIMINARIES 3 1 BASIC
DEFINITIONS AND NOTATION 3 2 MARTINGALES 7 3 THE POISSON PROCESS AND
BRBWNIAN MOTION 12 4 LEVY PROCESSES 19 5 WHY THE USUAL HYPOTHESES? 34 6
LOCAL MARTINGALES 37 7 STIELTJES INTEGRATION AND CHANGE OF VARIABLES 39
8 NAIVE STOCHASTIC INTEGRATION IS IMPOSSIBLE 43 BIBLIOGRAPHIC NOTES 44
EXERCISES FOR CHAPTER I 45 II SEMIMARTINGALES AND STOCHASTIC INTEGRALS
51 1 INTRODUCTION TO SEMIMARTINGALES 51 2 STABILITY PROPERTIES OF
SEMIMARTINGALES 52 3 ELEMENTARY EXAMPLES OF SEMIMARTINGALES 54 4
STOCHASTIC INTEGRALS 56 5 PROPERTIES OF STOCHASTIC INTEGRALS 60 6 THE
QUADRATIC VARIATION OF A SEMIMARTINGALE 66 7 ITO S FORMULA (CHANGE OF
VARIABLES) 78 8 APPLICATIONS OF ITO S FORMULA 84 BIBLIOGRAPHIC NOTES 92
EXERCISES FOR CHAPTER II 94 III SEMIMARTINGALES AND DECOMPOSABLE
PROCESSES 101 1 INTRODUCTION 101 2 THE CLASSIFICATION OF STOPPING TIMES
103 3 THE DOOB-MEYER DECOMPOSITIONS 105 4 QUASIMARTINGALES 116 XII
CONTENTS 5 COMPENSATORS 118 6 THE FUNDAMENTAL THEOREM OF LOCAL
MARTINGALES 124 7 CLASSICAL SEMIMARTINGALES 127 8 GIRSANOV S THEOREM 131
9 THE BICHTELER-DELLACHERIE THEOREM 143 BIBLIOGRAPHIC NOTES 147
EXERCISES FOR CHAPTER III 147 IV GENERAL STOCHASTIC INTEGRATION AND
LOCAL TIMES 153 1 INTRODUCTION 153 2 STOCHASTIC INTEGRATION FOR
PREDICTABLE INTEGRANDS 153 3 MARTINGALE REPRESENTATION 178 4 MARTINGALE
DUALITY AND THE JACOD-YOR THEOREM ON MARTINGALE REPRESENTATION 193 5
EXAMPLES OF MARTINGALE REPRESENTATION 200 6 STOCHASTIC INTEGRATION
DEPENDING ON A PARAMETER 205 7 LOCAL TIMES 210 8 AZEMA S MARTINGALE 227
9 SIGMA MARTINGALES 233 BIBLIOGRAPHIC NOTES 235 EXERCISES FOR CHAPTER IV
236 V STOCHASTIC DIFFERENTIAL EQUATIONS 243 1 INTRODUCTION 243 2 THE HJ
NORMS FOR SEMIMARTINGALES 244 3 EXISTENCE AND UNIQUENESS OF SOLUTIONS
249 4 STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS 257 5
FISK-STRATONOVICH INTEGRALS AND DIFFERENTIAL EQUATIONS 270 6 THE MARKOV
NATURE OF SOLUTIONS 291 7 FLOWS OF STOCHASTIC DIFFERENTIAL EQUATIONS:
CONTINUITY AND DIFFERENTIABILITY 301 8 FLOWS AS DIFFEOMORPHISMS: THE
CONTINUOUS CASE 310 9 GENERAL STOCHASTIC EXPONENTIALS AND LINEAR
EQUATIONS 321 10 FLOWS AS DIFFEOMORPHISMS: THE GENERAL CASE . 32 8 11
ECLECTIC USEFUL RESULTS ON STOCHASTIC DIFFERENTIAL EQUATIONS ... 338
BIBLIOGRAPHIC NOTES 347 EXERCISES FOR CHAPTER V 349 VI EXPANSION OF
FILTRATIONS 355 1 INTRODUCTION 355 2 INITIAL EXPANSIONS 356 3
PROGRESSIVE EXPANSIONS 369 4 TIME REVERSAL 377 BIBLIOGRAPHIC NOTES 383
EXERCISES FOR CHAPTER VI 384 CONTENTS XIII REFERENCES 389 SYMBOL INDEX
403 SUBJECT INDEX 407
|
| any_adam_object | 1 |
| author | Protter, Philip E. 1949- |
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| author_facet | Protter, Philip E. 1949- |
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| author_variant | p e p pe pep |
| building | Verbundindex |
| bvnumber | BV016523843 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.22.P76 2004 |
| callnumber-search | QA274.22.P76 2004 |
| callnumber-sort | QA 3274.22 P76 42004 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f MAT 605f |
| ctrlnum | (OCoLC)248898805 (DE-599)BVBBV016523843 |
| dewey-full | 519.2 519.222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.2 22 |
| dewey-search | 519.2 519.2 22 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:11:31Z |
| institution | BVB |
| isbn | 3540003134 |
| language | English |
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| physical | XIII, 415 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Protter, Philip E. 1949- Verfasser (DE-588)121454304 aut Stochastic integration and differential equations Philip E. Protter 2. ed. Berlin [u.a.] Springer 2004 XIII, 415 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 21 Literaturverz. S. 389 - 401 Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Martingal (DE-588)4126466-6 s Stochastisches Integral (DE-588)4126478-2 s Applications of mathematics 21 (DE-604)BV000895226 21 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Protter, Philip E. 1949- Stochastic integration and differential equations Applications of mathematics Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Martingal (DE-588)4126466-6 gnd |
| subject_GND | (DE-588)4126478-2 (DE-588)4057621-8 (DE-588)4126466-6 |
| title | Stochastic integration and differential equations |
| title_auth | Stochastic integration and differential equations |
| title_exact_search | Stochastic integration and differential equations |
| title_full | Stochastic integration and differential equations Philip E. Protter |
| title_fullStr | Stochastic integration and differential equations Philip E. Protter |
| title_full_unstemmed | Stochastic integration and differential equations Philip E. Protter |
| title_short | Stochastic integration and differential equations |
| title_sort | stochastic integration and differential equations |
| topic | Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral (DE-588)4126478-2 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Martingal (DE-588)4126466-6 gnd |
| topic_facet | Stochastic integrals Martingales (Mathematics) Stochastic differential equations Stochastisches Integral Stochastische Differentialgleichung Martingal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010211629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT protterphilipe stochasticintegrationanddifferentialequations |