Martingales and stochastic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1995
|
| Schriftenreihe: | Series on multivariate analysis
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 501 S. |
| ISBN: | 981022477X |
Internformat
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Datensatz im Suchindex
| _version_ | 1804125437211705344 |
|---|---|
| adam_text | SERIES ON .J MA RTINGALES AND STOCHASTIC ANALYSIS J. YEH DEPARTMENT OF
MATHEMATICS UNIVERSITY 0/ CALIFORNIA, IRVINE WORLD SCIENTIFIC SINGAPORE
* NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE V NOTATIONS XI 1
STOCHASTIC PROCESSES 1 §1 GENERATED A -ALGEBRAS 1 §2 STOCHASTIC
PROCESSES 11 [I] MEASURABLE AND PROGRESSIVELY MEASURABLE PROCESSES 11
[II] PREDICTABLE PROCESSES 19 §3 STOPPING TIMES 25 [I] STOPPING TIMES
FOR STOCHASTIC PROCESSES WITH CONTINUOUS TIME . . . . 25 [II] STOPPING
TIMES FOR STOCHASTIC PROCESSES WITH DISCRETE TIME 39 [III] RANDOM
VARIABLES AT STOPPING TIMES 41 [IV] STOPPED PROCESSES AND TRUNCATED
PROCESSES 45 §4 CONVERGENCE IN L P AND UNIFORM INTEGRABILITY 49 [I]
CONVERGENCE IN L P 49 [II] UNIFORMLY INTEGRABLE SYSTEMS OF RANDOM
VARIABLES 53 2 MARTINGALES 71 §5 MARTINGALE, SUBMARTINGALE AND
SUPERMARTINGALE 71 [I] MARTINGALE, SUBMARTINGALE AND SUPERMARTINGALE
PROPERTIES 71 [II] CONVEXITY THEOREMS 76 [IIIJ DISCRETE TIME INCREASING
PROCESSES AND DOOB DECOMPOSITION . . . . 78 [IV] MARTINGALE TRANSFORM 81
[V] SOME EXAMPLES 84 §6 FUNDAMENTAL SUBMARTINGALE INEQUALITIES 86 [I]
OPTIONAL STOPPING AND OPTIONAL SAMPLING 87 [II] MAXIMAL AND MINIMAL
INEQUALITIES 93 [III] UPCROSSING AND DOWNCROSSING INEQUALITIES 101 VN
VIII CONTENTS §7 CONVERGENCE OF SUBMARTINGALES 110 [I] CONVERGENCE OF
SUBMARTINGALES WITH DISCRETE TIME 110 [II] CONVERGENCE OF SUBMARTINGALES
WITH CONTINUOUS TIME 114 [III] CLOSING A SUBMARTINGALE WITH A FINAL
ELEMENT 116 [IV] DISCRETE TIME 1,2-MARTINGALES 119 §8 UNIFORMLY
INTEGRABLE SUBMARTINGALES 122 [I] CONVERGENCE OF UNIFORMLY INTEGRABLE
SUBMARTINGALES 122 [II] SUBMARTINGALES WITH REVERSED TIME 124 [HI]
OPTIONAL SAMPLING BY UNBOUNDED STOPPING TIMES 131 [IV] UNIFORM
INTEGRABILITY OF RANDOM VARIABLES AT STOPPING TIMES . . . . 141 §9
REGULARITY OF SAMPLE FUNCTIONS OF SUBMARTINGALES 145 [I] SAMPLE
FUNCTIONS OF RIGHT-CONTINUOUS SUBMARTINGALES 145 [II] RIGHT-CONTINUOUS
MODIFICATION OF A SUBMARTINGALE 149 §10 INCREASING PROCESSES 155 [I] THE
LEBESGUE STIELTJES INTEGRAL 155 [II] INTEGRATION WITH RESPECT TO
INCREASING PROCESSES 158 [III] DOOB-MEYER DECOMPOSITION 171 [IV] REGULAR
SUBMARTINGALES 187 3 STOCHASTIC INTEGRALS 197 §11 L2-MARTINGALES AND
QUADRATIC VARIATION PROCESSES 197 [I] THE SPACE OF RIGHT-CONTINUOUS
^-MARTINGALES 197 [II] SIGNED LEBESGUE-STIELTJES MEASURES 205 [III]
LOCALLY BOUNDED VARIATION PROCESSES 207 [IV] QUADRATIC VARIATION
PROCESSES 212 §12 STOCHASTIC INTEGRALS WITH RESPECT TO MARTINGALES , 221
[I] STOCHASTIC INTEGRAL OF BOUNDED LEFT-CONTINUOUS ADAPTED SIMPLE
PROCESSES W. R. T. L 2 -MARTINGALES 222 [II] STOCHASTIC INTEGRAL OF
PREDICTABLE PROCESSES W. R. T. I^-MARTINGALES . . 235 §13 ADAPTED
BROWNIAN MOTIONS 262 [I] PROCESSES WITH INDEPENDENT INCREMENTS 262 [II]
BROWNIAN MOTIONS IN R D 270 [III] 1-DIMENSIONAL BROWNIAN MOTIONS 286
[IV] STOCHASTIC INTEGRALS WITH RESPECT TO A BROWNIAN MOTION 290 §14
EXTENSIONS OF THE STOCHASTIC INTEGRAL 297 [I] LOCAL I^-MARTINGALES AND
THEIR QUADRATIC VARIATION PROCESSES 297 [II] EXTENSIONS OF THE
STOCHASTIC INTEGRAL TO LOCAL MARTINGALES 306 CONTENTS IX §15 ITO S
FORMULA 318 [I] CONTINUOUS LOCAL SEMIMARTINGALES AND ITO S FORMULA 318
[II] STOCHASTIC INTEGRALS WITH RESPECT TO QUASIMARTIGALES 333 [III]
EXPONENTIAL QUASIMARTINGALES 335 [IV] MULTIDIMENSIONAL ITO S FORMULA 340
§16 ITO S STOCHASTIC CALCULUS 344 [I] THE SPACE OF STOCHASTIC
DIFFERENTIALS 344 [II] FISK-STRATONOVICH INTEGRALS 352 4 STOCHASTIC
DIFFERENTIAL EQUATIONS 357 §17 THE SPACE OF CONTINUOUS FUNCTIONS 357 [I]
FUNCTION SPACE REPRESENTATION OF CONTINUOUS PROCESSES 357 [II]
METRIZATION OF THE SPACE OF CONTINUOUS FUNCTIONS 364 §18 DEFINITION AND
FUNCTION SPACE REPRESENTATION OF SOLUTION 368 [I] DEFINITION OF
SOLUTIONS 368 [II] FUNCTION SPACE REPRESENTATION OF SOLUTIONS 372 [III]
INITIAL VALUE PROBLEMS 385 §19 EXISTENCE AND UNIQUENESS OF SOLUTIONS 395
[I] UNIQUENESS IN PROBABILITY LAW AND PATHWISE UNIQUENESS OF SOLUTIONS .
395 [II] SIMULTANEOUS REPRESENTATION OF TWO SOLUTIONS ON A FUNCTION
SPACE . . 405 §20 STRONG SOLUTIONS 419 [I] EXISTENCE OF STRONG SOLUTIONS
419 [II] UNIQUENESS OF STRONG SOLUTIONS 432 A STOCHASTIC INDEPENDENCE
443 B CONDITIONAL EXPECTATIONS 453 C REGULAR CONDITIONAL PROBABILITIES
475 D MULTIDIMENSIONAL NORMAL DISTRIBUTIONS 487 BIBLIOGRAPHY 495 INDEX *
498
|
| any_adam_object | 1 |
| author | Yeh, James |
| author_facet | Yeh, James |
| author_role | aut |
| author_sort | Yeh, James |
| author_variant | j y jy |
| building | Verbundindex |
| bvnumber | BV010950043 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.5.Y44 1995 |
| callnumber-search | QA274.5.Y44 1995 |
| callnumber-sort | QA 3274.5 Y44 41995 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f MAT 605f |
| ctrlnum | (OCoLC)33243595 (DE-599)BVBBV010950043 |
| dewey-full | 519.2/8720 519.2/87 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/87 20 519.2/87 |
| dewey-search | 519.2/87 20 519.2/87 |
| dewey-sort | 3519.2 287 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:33Z |
| institution | BVB |
| isbn | 981022477X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007323888 |
| oclc_num | 33243595 |
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| physical | XIII, 501 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on multivariate analysis |
| series2 | Series on multivariate analysis |
| spelling | Yeh, James Verfasser aut Martingales and stochastic analysis J. Yeh Singapore [u.a.] World Scientific 1995 XIII, 501 S. txt rdacontent n rdamedia nc rdacarrier Series on multivariate analysis 1 Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Martingal (DE-588)4126466-6 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Stochastische Analysis (DE-588)4132272-1 s Series on multivariate analysis 1 (DE-604)BV010950028 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007323888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yeh, James Martingales and stochastic analysis Series on multivariate analysis Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4126466-6 (DE-588)4057630-9 |
| title | Martingales and stochastic analysis |
| title_auth | Martingales and stochastic analysis |
| title_exact_search | Martingales and stochastic analysis |
| title_full | Martingales and stochastic analysis J. Yeh |
| title_fullStr | Martingales and stochastic analysis J. Yeh |
| title_full_unstemmed | Martingales and stochastic analysis J. Yeh |
| title_short | Martingales and stochastic analysis |
| title_sort | martingales and stochastic analysis |
| topic | Analyse stochastique ram Martingales (mathématiques) ram Martingales (Mathematics) Stochastic analysis Stochastische Analysis (DE-588)4132272-1 gnd Martingal (DE-588)4126466-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Analyse stochastique Martingales (mathématiques) Martingales (Mathematics) Stochastic analysis Stochastische Analysis Martingal Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007323888&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010950028 |
| work_keys_str_mv | AT yehjames martingalesandstochasticanalysis |